Gemcitabine Hydrochloride Alone or With M6620 in Treating Patients With Recurrent Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Patients must have histologically confirmed high grade serous ovarian or primary peritoneal or fallopian tube cancer; platinum resistant disease is defined as progression within 6 months after last platinum 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 \>= 20 mm (\>= 2 cm) with conventional techniques or as \>= 10 mm (\>= 1 cm) with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam; measurable disease by RECIST version (v)1.1 with at least one measurable target lesion

Prior therapy: No line limit but no more than 1 prior regimens in the platinum resistant setting; no prior treatment targeting the ATR/checkpoint kinase 1 (CHK1) pathway and no prior gemcitabine as single agent; hormonal therapies immunotherapy, and antiangiogenic therapies (as single agents) do not count as lines; poly (adenosine diphosphate \[ADP\]-ribose) polymerases (PARP)-inhibitors count as a line of therapy unless given in the maintenance setting; PARP-inhibitors given as maintenance after platinum therapy do not count as a line of therapy; prior carboplatin/gemcitabine is allowed provided that there was no disease progression within 12 months after completion of the carboplatin/gemcitabine regimen; subjects may begin protocol treatment at least 4 weeks or 5 half-lives, whichever is shorter, after their last dose of chemotherapy or hormonal therapy, assuming they are otherwise eligible

Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 (Karnofsky \>= 70%)

Life expectancy of greater than 6 months

Leukocytes \>= 3,000/mcL (within 2 weeks prior to initiation of study treatment)

Absolute neutrophil count \>= 1,500/mcL (within 2 weeks prior to initiation of study treatment)

Platelets \>= 100,000/mcL (within 2 weeks prior to initiation of study treatment)

Total bilirubin within normal institutional limits (within 2 weeks prior to initiation of study treatment)

Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (within 2 weeks prior to initiation of study treatment)

Creatinine =\< upper limit of institutional normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal (within 2 weeks prior to initiation of study treatment)

Confirmation of availability of a formalin-fixed, paraffin-embedded (FFPE) tumor specimen with adequate tumor tissue (either one paraffin embedded tissue block OR 10 5-micron unstained slides from the block on regular \[non-plus\] slides and 1 hematoxylin and eosin \[H\&E\] slide)

All acute, clinically significant treatment-related toxicity from prior therapy, except for alopecia, must have resolved to grade =\< 1 prior to study entry

At least 4 weeks since major surgery or radiation therapy

The effects of M6620 (VX-970) on the developing human fetus are unknown; for this reason and because deoxyribonucleic acid (DNA) damage inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and 6 months after completion of study; 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

No known hypersensitivity or contraindication to the components of study treatment (M6620 \[VX-970\], gemcitabine)

Ability to understand and the willingness to sign a written informed consent document

What this study is about