Gemcitabine Hydrochloride With or Without WEE1 Inhibitor MK-1775 in Treating Patients With Recurrent Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed epithelial ovarian, primary peritoneal and fallopian tube carcinoma; all histologic subtypes of epithelial ovarian cancer are eligible, but only patients with high grade serous ovarian cancer will be considered for the statistical analysis; non-high grade serous cancers will be allowed in an exploratory cohort * Patients must be platinum-resistant (platinum-free interval \< 6 months) or have platinum-refractory disease as per Gynecologic Cancer Intergroup Committee (GCIC) criteria; disease progression has to be radiologic or clinical; biomarker progression with CA125 after a platinum based regimen would not be sufficient evidence of disease progression; the patients must have had radiological progression to that regimen * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \> 10 mm with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * There is no limitation in the number of prior lines of therapy * Patients must have completed any prior chemotherapy, radiotherapy or major surgery at least 4 weeks before receiving study treatment; ongoing toxicities related to treatment must be =\< grade 1 and patients with grade 2 alopecia or peripheral neuropathy can also be included; palliative ra…