Non-covalent BTK Inhibitor Nemtabrutinib in Combination With the CD20 Monoclonal Antibody Rituximab for the Treatment of Marginal Zone Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Diagnosis of MZL including splenic marginal zone lymphoma (SMZL), extra nodal marginal zone lymphoma (ENMZL) and nodal marginal zone lymphoma (NMZL), established by histologic assessment * Requiring treatment for MZL. Patients receiving prior systemic therapy as well as treatment naïve patients are eligible * Local radiotherapy not exceeding a total dose of 20 Gy at least 2 weeks prior the first dose of study therapy is allowed * Radiographically measurable lymphadenopathy or extra nodal lymphoid malignancy (as defined by Lugano Classification for non-Hodgkin lymphoma \[NHL\]) * Subjects with splenic MZL who do not meet the radiographically measurable disease criteria described herein are eligible for participation provided that bone marrow infiltration of MZL is histologically confirmed * Subjects with skin extranodal marginal zone lymphoma (EMZL) who do not meet the radiographically measurable disease criteria described herein are eligible provided that skin lesion measures ≥ 1.5 cm in diameter and is documented by photo or there are multiple skin lesions measuring \> 1cm in diameter on the body that cannot be incorporated in one radiation field and at least one of them is histologically confirmed as MZL * Subjects with gastric extra nodal MZL histologically confirmed and need therapy but do not have measurable disease and in which response to treatment can be assess by multiple random gastric biopsies * Subjects with conjunctival EMZL who do not meet the radiographically measurable disease criteria described herein are eligible provided that conjunctival lesion measures ≥ 1 cm in diameter and is documented by photo or there are multiple conjunctival lesions measuring together \> 1 5cm that cannot be treated by radiation because of previous radiation therapy, contraindications to radiation and patient refusal to receive radiation therapy. At least one of these lesions needs be histologically confirmed as MZL * Willing to provide a lymph node or tissue biopsy from the most recent available archival tissue or undergo an incisional or excisional lymph node or tissue biopsy * Subjects with splenic MZL who do not have a tumor to biopsy or an archival tumor tissue sample are eligible provided subject is willing to undergo a bone marrow biopsy or provide an archival bone marrow biopsy that was obtained before the date of the first dose of study treatment; bone marrow sample must show histologically confirmed infiltration of MZL * At least one of the following criteria for treatment initiation: * Involvement of ≥ 3 nodal sites, each with diameter of ≥ 3 cm * Any nodal or extra nodal tumor mass with a diameter of ≥ 5 cm * B symptoms (fever ≥ 38 degrees Celsius of unclear etiology, night sweats, weight loss \> 10% within the prior 6 months) or other symptoms attributed to disease or specific organ involvement associated with the relapse * Risk of local compressive symptoms that may result in organ compromise * Splenomegaly or splenic lesion without splenomegaly * Leukopenia attributed to MZL (leukocytes \< 1000/mm\^3) * Leukemia (\> 5,000 lymphoma cells/mm\^3) * Threatened organ function, especially for extra nodal MZL * Requirement for transfusion or growth factor support attributed to lymphoma * Involvement of 2 or more extra nodal sites, with tumor/lesion in each extra nodal site ≥ 1 cm * Progression or relapsed within 24 months after MZL diagnosis in patients previously treated with ≥ 1 line of systemic therapy * Life expectancy \> 3 months * Prior adverse events (AEs) must be resolved to grade 1 * Without bone marrow involvement: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * With bone marrow involvement: ANC ≥ 500/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Platelets ≥ 50,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement. * With bone marrow involvement: Platelets ≥ 30,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement. * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * Subjects with documented history of Gilbert's syndrome and in whom total bilirubin elevations are accompanied by elevated indirect bilirubin are eligible * Hemoglobin ≥ 8.0 g/dL * Aspartate aminotransferase (AST) ≤ 2.5 x ULN or ≤ 5 x ULN in the presence of liver involvement by lymphoma * Alanine aminotransferase (ALT) ≤ 2.5 x ULN or ≤ 5 x ULN in the presence of liver involvement by lymphoma * Creatinine clearance of ≥ 45 mL/min/1.73 m\^2 using the Modification of Diet in Renal Disease formula OR ≥ 45 mL/min by the Cockcroft-Gault formula * Seronegative for hepatitis C virus (HCV), hepatitis B virus (HBV) (surface antigen negative) OR * If seropositive for HBV or HCV, nucleic acid quantitation must be performed. Viral load must be undetectable. Patients with occult or prior HBV infection (defined as negative hepatitis B virus surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) may be included if HBV deoxyribonucleic acid (DNA) is undetectable, if they are willing to undergo DNA testing on day 1 of every cycle and every three months for at least 12 months after the last cycle of study treatment * Participants with HIV are eligible if they meet ALL the following: * CD4 count \> 350 cells/µL at screening * The HIV viral load is below the detectable level as per locally available testing * Are on a stable antiretroviral therapy (ART) regimen for at least 4 weeks prior to study entry * NOTE: ART includes drugs, which are NOT strong cytochrome P450 (CYP)3A4 inducers (participants receiving ART that are strong CYP3A4 inducers are not eligible to be included in the study) * HIV screening tests are not required unless: * Known history of HIV infection * As mandated by local health authority * Are compliant with their ART * NOTE: If the participant has had an AIDS defining opportunistic infection in the past 12 months prior to screening, they are not eligible to be included in the study * Person of childbearing potential (POCBP): Negative urine or serum pregnancy test * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Participants assigned male sex at birth: * If capable of producing sperm, the participant agrees to the following during the intervention period and for at least the time needed to eliminate each study intervention after the last dose of study intervention. The length of time required to continue contraception for each study intervention is: * Nemtabrutinib: 12 days * Rituximab: 3 months * Abstains from penile-vaginal intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) and agrees to remain abstinent OR * Uses contraception as detailed below unless confirmed to be azoospermic (vasectomized or secondary to medical cause, documented from the site personnel's review of the participant's medical records, medical examination, or medical history interview) as detailed below: * Uses a penile/external condom plus nonparticipant of childbearing potential who is not currently pregnant and should also be advised of the benefit for that partner to use an additional method of contraception, as a condom may break or leak * Note: Participants capable of producing ejaculate whose partner is pregnant or breastfeeding must agree to use penile/external condom during each episode of sexual activity in which the partner is at risk of drug exposure via ejaculate * Contraceptive use by participants capable of producing sperm should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions are more stringent than the requirements above, the local label requirements are to be followed * Participants assigned female sex at birth: * A participant assigned female sex at birth is eligible to participate if not pregnant or breastfeeding, and at least one of the following conditions applies: * Is not a person of childbearing potential (POCBP) OR * Is a POCBP and: * Uses a contraceptive method that is highly effective (with a failure rate of \< 1% per year), with low user dependency, or is abstinent from penile-vaginal intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis), during the intervention period and for at least the time needed to eliminate each study intervention after the last dose of study intervention. The length of time required to continue contraception for each study intervention is: * Nemtabrutinib: 1 month * Rituximab: 12 months * The investigator should evaluate the potential for contraceptive method failure (ie, noncompliance, recently initiated) in relationship to the first dose of study intervention. Contraceptive use by POCBPs should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions are more stringent than the requirements above, the local label requirements are to be followed. * Has a negative highly sensitive pregnancy test (urine or serum) as required by local regulations within 24 hours (for urine test) or 72 hours (for serum test) before the first dose of study intervention. If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive * Abstains from breastfeeding during the study intervention period and for at least 30 days after study intervention with nemtabrutinib * Medical history, menstrual history, and recent sexual activity has been reviewed by the investigator to decrease the risk for inclusion of a POCBP with an early undetected pregnancy * Patients with gastrointestinal dysfunction and/or clinically significant medical condition of malabsorption, inflammatory bowel disease, chronic conditions which manifest with diarrhea, refractory nausea, vomiting or any other condition that will interfere significantly with drug absorption (e.g., gastric bypass surgery, gastrectomy) Exclusion Criteria: * Evidence of diffuse large B-cell lymphoma (DLBCL) transformation * Subjects with presumptive evidence of transformation based on clinical assessment of factors such as, but not limited to, increasing lactate dehydrogenase, rapidly worsening disease, or frequent B-symptoms, must be ruled out for a transformation to a more aggressive disease, such as DLBCL * History of central nervous system lymphoma (either primary or metastatic) or leptomeningeal disease * Active graft versus host disease * Concurrent anticancer therapy (eg, chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, hormonal therapy, investigational therapy, or tumor embolization) * Allogeneic stem cell transplant within the last 6 months, or autologous stem cell transplant within the last 3 months before the date of the first dose of study treatment * Receipt of anticancer medications or investigational drugs within the following intervals before the date of the first dose of study treatment: * \< 10 weeks from completion of any radio- or toxin-immunoconjugates * \< 4 weeks for immunotherapy * \< 3 weeks for radiotherapy * \< 2 weeks for any investigational agent or other anticancer medications * Steroids that are used for treatment of allergy or other underlying condition are permittable, but not steroids started to treat lymphoma. Subjects receiving corticosteroids must be at a dose level ≤ 10 mg/day within 7 days of the study treatment administration * Inadequate recovery from adverse events related to prior therapy to grade ≤ 1 (excluding grade 2 alopecia and neuropathy) * Prior non-covalent BTK inhibitor (prior covalent BTK inhibitors are allowed) * Major surgery (under general anesthesia) within 30 days prior to therapy initiation * Live vaccine within 30 days * Use of strong cytochrome P450 3A4 (CYP3A4) inhibitors or inducers within 2 weeks of the first day of study therapy * History of prior malignancy except: * Malignancy treated with curative intent and no known active disease present for ≥ 2 years prior to initiation of therapy * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease * Adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease * Asymptomatic prostate cancer managed with "watch and wait" strategy * Superficial bladder cancer * Myelodysplastic syndrome which is clinically well controlled and no evidence of the cytogenetic abnormalities characteristic of myelodysplasia on the bone marrow at screening * History of severe bleeding disorder defined as an ongoing congenital or acquired condition that leads to an increased likelihood of bleeding * Unstable cardiac disease as defined by one of the following: * Acute myocardial infarction (MI) within the past 6 months * NYHA (New York Heart Association) heart failure class III * Unstable angina (angina symptoms at rest) or new-onset angina (begun within the last 3 months) * Left ventricular ejection fraction (LVEF) \< 45% * Corrected QT interval (QTc) prolongation (defined as a Fridericia's formula-corrected QT interval \[QTcF\] \> 450 msecs) or other significant electrocardiogram (ECG) abnormalities including second degree atrioventricular (AV) block type II, third degree AV block, or bradycardia (ventricular rate less than 50 beats/min) * AIDS-defining opportunistic infection in the past 12 months prior to screening * History or concurrent condition of interstitial lung disease and/or severely impaired lung function * Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before the start of study treatment * History of organ transplant * Known allergy/sensitivity to nemtabrutinib or any of the excipients; history of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents * Clinically significant uncontrolled illness * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment or any major episode of infection (as evaluated by the investigator) within 4 weeks prior to the first study treatment * Primary or secondary central nervous system (CNS) lymphoma at the time of recruitment or history of CNS lymphoma * POCBP: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)