Trametinib in Treating Patients With Recurrent or Progressive Low-Grade Ovarian Cancer or Peritoneal Cavity Cancer

Inclusion Criteria: * Patients age greater than 18 with the following tumors are included in the study: * Patients initially diagnosed with low-grade serous ovarian or peritoneal carcinoma that recur as low-grade serous carcinoma (invasive micropapillary serous carcinoma or invasive grade I serous carcinomas as defined by GOG, Federation of Obstetricians and Gynecologists \[FIGO\], World Health Organization \[WHO\] or Silverberg) * Patients initially diagnosed with serous borderline ovarian or peritoneal carcinoma that recur as low-grade serous carcinoma (invasive micropapillary serous carcinoma or invasive grade I serous carcinomas as defined by GOG, FIGO WHO or Silverberg) * At least 4 weeks must have elapsed since the patient underwent any major surgery (e.g. MAJOR: laparotomy, laparoscopy, thoracotomy, VATS \[video assisted thorascopic surgery\]); there is no restriction on MINOR procedures: (e.g. central venous catheter placement, ureteral stent placement or exchange, tumor core or fine-needle aspirate \[FNA\] biopsy) * Patients must have documented low-grade serous carcinoma; confirmation must occur by prospective pathology review prior to study entry; the prospective pathology review can be done on tissue from the recurrent carcinoma or from original diagnostic specimen * All patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; measurable disease is defined as at least one target lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI), or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI; all imaging studies must be performed within 28 days prior to registration * Prior therapy * Patients must have recurred or progressed following at least one platinum-based chemotherapy regimen * Patients may have received an unlimited number of prior therapy regimens * Patients may not have received all of the five choices in the "standard therapy" arm * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration * Any other prior therapy directed at the malignant tumor, including chemotherapy and radiation therapy, must be discontinued at least 4 weeks prior to registration; any investigational agent must be discontinued at least 28 days prior to registration * Trametinib, can cause fetal harm when administered to a pregnant woman; women of child-bearing potential (i.e. patients whose reproductive organs remain in place and who have not passed menopause) and men must agree to use a highly effective method of contraception (e.g. hormonal, intrauterine device or; abstinence\*) prior to study entry, during the study participation, and for six months after the last dose of the drug; women of child-bearing potential must have a negative serum pregnancy test within 14 days prior to randomization, cannot be breast-feeding, and must agree to use a highly effective form of contraception throughout the treatment period and for 6 months after the last dose of study treatment; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Abstinence is only acceptable when this is in line with the preferred and usual lifestyle of the patient * Patients must have the ability to understand and sign an approved informed consent and authorization permitting release of personal health information * Patients must have a GOG performance status of 0 or 1 * Able to swallow and retain orally-administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption, such as malabsorption syndrome, bowel obstruction, or major resection of the stomach or bowel * All prior treatment-related toxicities must be CTCAE v4 grade =\< 1 (except alopecia) at the time of randomization * Patients must have a left ventricular ejection fraction \>= lower limit of normal by echocardiogram (ECHO) or multigated acquisition scan (MUGA) * Serum creatinine =\< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault formula) \>= 50 mL/min OR 24-hour urine creatinine clearance \>= 50 mL/min (within 14 days prior to treatment) * Bilirubin =\< 1.5 times upper limit of normal (within 14 days prior to treatment) * Alanine aminotransferase (ALT) =\< 2.5 times upper limit of normal (within 14 days prior to treatment) * Aspartate aminotransferase (AST) =\< 2.5 times upper limit of normal (within 14 days prior to treatment) * Albumin \>= 2.5 g/dL (within 14 days prior to treatment) * Prothrombin time (PT) and activated partial thromboplastin time (APTT) =\< 1.5 times upper limit of normal (within 14 days prior to treatment) * Neutrophil count \>= 1.5 x 10\^9/L (within 14 days prior to treatment) * Platelet count \>= 100 x 10\^9/L (within 14 days prior to treatment) * Hemoglobin \>= 9.0 g/dL (within 14 days prior to treatment) * If letrozole is selected as the control therapy, patients must be postmenopausal, either following bilateral oophorectomy or at least 5 years after spontaneous menopause; patients within 5 years of spontaneous menopause or who have had a hysterectomy without bilateral oophorectomy must have postmenopausal luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels; patients on hormone replacement therapy (HRT) must agree to withdrawal of hormone therapy before letrozole is started Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Use of other investigational drugs within 28 days (or five half-lives, whichever is shorter; with a minimum of 14 days from the last dose) preceding the first dose of trametinib or standard of care agent * If patients have had a potential index lesion radiated, it must have progressed post radiation therapy to be used as a measurable eligibility lesion * Patients may not have received prior MEK, v-Ki-ras2 Kirsten rat sarcoma viral oncogene homolog (KRAS), or v-raf murine sarcoma viral oncogene homolog B1 (BRAF) inhibitor therapy * Current use of a prohibited medication; the following medications or non-drug therapies are prohibited: * Patients may not be receiving any other anti-cancer or investigational agents * Because the composition, PK, and metabolism of many herbal supplements are unknown, the concurrent use of all herbal supplements is prohibited during the study (including, but not limited to St. John's wort, kava, ephedra \[ma huang\], gingko biloba, dehydroepiandrosterone \[DHEA\], yohimbe, saw palmetto, or ginseng) * Patients with known leptomeningeal or brain metastases or spinal cord compression should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * Patients with a bowel obstruction or any other gastrointestinal condition that might affect absorption of the oral drug should be excluded; this would include patients with inability to swallow and retain orally-administered medication, malabsorption syndrome, or those with a major resection of the stomach or bowels * Patients with a history of interstitial lung disease or pneumonitis * Patients with a previous or current malignancy at other sites should be excluded, with the exception of: * Curatively treated local tumors such as carcinoma-in-situ of the cervix, basal or squamous cell carcinoma of the skin * Tumors for which no relapse has been observed within 5 years * Known hepatitis B virus (HBV), or hepatitis C virus (HCV) infection (patients with chronic or cleared HBV and HCV infection are eligible); patients with human immunodeficiency virus (HIV) are not eligible if on anti-retroviral medications * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients, or to dimethyl sulfoxide (DMSO), or to Cremophor EL (polyoxyethylated castor oil); please note, exclusion for Cremophor is unnecessary unless paclitaxel is the only agent available and the patient randomizes to the conventional therapy option * Patients with a history or evidence of cardiovascular risk, including any of the following: * Left ventricular ejection fraction (LVEF) \< lower limit of normal (LLN) * Bazett's corrected QT (QTcB) \>= 480 msec * History or evidence of current clinically significant uncontrolled arrhythmias * Exception: Subjects with controlled atrial fibrillation for \> 30 days prior to randomization are eligible * History of (within 6 months prior to randomization) acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting * History or evidence of current \>= class II congestive heart failure as defined by New York Heart Association (NYHA) * Treatment refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mmHg which cannot be controlled by anti-hypertensive therapy * Patients with intra-cardiac defibrillators or permanent pacemakers * Known cardiac metastases * Patients with a history or current evidence/risk of retinal vein occlusion (RVO) * Any serious and/or unstable pre-existing medical disorder (aside from malignancy exception above), psychiatric disorder, or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures * Patients who require use of a concomitant medication that can prolong the QT interval * Animal reproductive studies have not been conducted with trametinib; therefore, the study drug must not be administered to pregnant women or nursing mothers; women of childbearing potential should be advised to avoid pregnancy and use effective methods of contraception; if a female patient or a female partner of a patient becomes pregnant while the patient receives trametinib, the potential hazard to the fetus should be explained to the patient and partner (as applicable)