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 radiation to \< 10% of bone marrow is permissible if completed within one week of commencing study treatment as long as the toxicities secondary to palliative radiotherapy are limited to grade 1; the lesions that have received radiation treatment immediately before will be excluded as target lesions; previously irradiated lesions can be considered as targeted lesions, as long as there is prove of radiological progression
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 3 months
* Leukocytes \>= 3,000/mcL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Hemoglobin \>= 90 g/L

  * Blood transfusions are allowed at any time during the screening, treatment or follow-up period, according to the center recommendations
* Prothrombin time (PT), partial thromboplastin time (PTT) and international normalized ratio (INR) =\< 1.5 upper limit of normal (ULN)
* Total bilirubin =\< 1.5 x institutional upper limit of normal; unless due to Gilbert's syndrome
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal (5 x if liver metastases)
* Creatinine =\< 1.5 × institutional upper limit of normal OR creatinine clearance \>= 40 mL/min/1.73 m\^2 for patients with creatinine levels above 1.5 x institutional limit of normal
* Patients must be able to tolerate oral medication and not have evidence of active bowel obstruction

  * Note: patients can have a history of prior bowel obstruction, provided the patient is not having symptoms of bowel obstruction at the time of enrolment and the bowel obstruction is not anticipated to recur during the participation in the study
* Patients must have disease amenable to biopsy and must be willing to undergo a paired biopsy for correlative analyses (the first biopsy within 28 days prior to start of treatment and the second biopsy while on treatment)
* Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately

  * Women of childbearing potential include women who have experienced menarche and who have not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are not postmenopausal; postmenopause is defined as amenorrhea \>= 12 consecutive months; Note: women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, anti-estrogens, ovarian suppression or any other reversible reason
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who previously received gemcitabine for the treatment of recurrent disease
* Patients who are receiving any other investigational agents
* Patients with clinically or radiologically unstable brain metastases are excluded from this clinical trial

  * Note: patients with stable brain metastases after treatment, for at least 3 months prior to enrolling on this trial, could participate in the study; patients should be off, or on a stable dose of steroids
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD 1775 (MK-1775) or gemcitabine
* Patients taking the following prescription or non-prescription drugs or other products (i.e. grapefruit juice) are ineligible: sensitive cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) substrates, CYP3A4 substrates with a narrow therapeutic index, moderate to potent inhibitors/inducers of CYP3A4; patients would be eligible if the medications can be discontinued two weeks prior to day 1 of dosing and withheld throughout the study until 2 weeks after the last dose of study medication
* Pregnant and breastfeeding women are excluded from this study
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible
* Uncontrolled intercurrent illness including, but not limited to, myocardial infarction within 6 months, congestive heart failure, symptomatic congestive heart failure, unstable angina pectoris, active cardiomyopathy, unstable ventricular arrhythmia, uncontrolled hypertension, uncontrolled psychotic disorders, serious infections, active peptic ulcer disease, active liver disease or cerebrovascular disease with previous stroke, or psychiatric illness/social situations that would limit compliance with study requirements