Imatinib and Rituximab in Treating Cutaneous Sclerosis in Patients With Chronic Graft-Versus-Host Disease

Inclusion Criteria: * Diagnosis within the past 18 months of cutaneous sclerosis after hematopoietic cell transplant (HCT) with sclerotic skin, morphea, myofascial involvement or joint contractures; must have a score of 2 or greater on the Vienna skin scale in any area, or a range-of-motion (ROM) score of 5 or less at the shoulder, elbow or wrist, or 3 or less at the ankle * No medication added for the treatment of graft versus host disease (GVHD) within the past 4 weeks * Receiving corticosteroids at a dose greater than required for treatment of adrenal insufficiency, unless the physician documents why steroids are contraindicated * Age 2-99 years * Karnofsky performance status \>= 60% at enrollment * All females of childbearing potential must have a negative serum or urine pregnancy test =\< 7 days prior to starting study therapy * All females of childbearing potential must agree to use a form of Food and Drug Administration (FDA) approved contraception from enrollment to one month after study treatment ends * Subject has the ability to understand and willingness to sign a written informed consent document Exclusion Criteria: * Total bilirubin \> 1.5x upper limit of normal (ULN) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 x ULN * Renal insufficiency (serum creatinine \> 2.0 mg/dl) * Platelets \< 30,000/ul or absolute neutrophil count \< 1500/ul * Known hypersensitivity to rituximab or other anti-B cell antibodies * Known imatinib intolerance or allergy * Evidence of any active viral, bacterial, or fungal infection that is progressive despite appropriate treatment * Hepatitis B surface antigen positive * Hepatitis B core antibody positive, unless hepatitis B virus (HBV) deoxyribonucleic acid (DNA) is undetectable * Hepatitis C antibody positive, unless hepatitis C virus (HCV) ribonucleic acid (RNA) is undetectable * Pregnant, lactating, or planning a pregnancy while in the study * Distal leg skin score 3 or higher as the only manifestation of sclerosis * Prior treatment of chronic GVHD with imatinib, rituximab, or any other monoclonal B-cell antibody (e.g. ofatumumab) * Receipt of imatinib within the previous 6 months for any indication * Receipt of any monoclonal B-cell antibody (e.g. rituximab, ofatumumab) within the previous 12 months for any indication * Treatment with anti-B-cell cellular therapy (e.g. chimeric antigen-receptor-engineered cells) at any time after transplant * Current treatment with extracorporeal photopheresis (ECP) at the time of enrollment * History of psychiatric disorder that would interfere with normal participation in this study * Inability or unwillingness of subject and/or parent guardian to provide informed consent or comply with study protocol * Use of non-FDA approved drugs within 4 weeks of participation * Patient with any condition that, in the opinion of the investigator, would interfere with the subject's ability to comply with the study requirements * Patients with uncontrolled substance abuse