Birinapant and Carboplatin in Treating Patients and Targeting Recurrent High Grade Ovarian, Fallopian Tube, or Primary Peritoneal Cancer (HGSOC)

Inclusion Criteria: * All patients must have measurable disease by imaging defined as tumor that can be measured \>= 10 mm with multiparametric magnetic resonance imaging (MRI) (primary modality of imaging) or computed tomography (CT) (as an alternative) or \>= 10 mm by caliper on physical examination * Participant is capable of understanding and complying with parameters as outlined in the protocol and able to sign and date the informed consent, approved by an Independent Ethics Committee (IEC)/Institutional Review Board (IRB), prior to initiation of any screening or study-specific procedures * The participant must have a histologic diagnosis of recurrent high grade serous ovarian cancer (ovarian, tubal, peritoneal), to be treated with chemotherapy * Participants must have an image guided biopsy performed to yield fresh tissue for the in vitro organoid bio-assay and two biomarker testing (western blot and immunohistochemistry) * Only patients with tumors that score positive in the in vitro organoid bio-assay will be enrolled in the clinical trial; patients with tumors that score negative in this bio-assay will be considered screening failures and will not be enrolled in the clinical trial * Participant must have either no neuropathy (sensory and motor) or neuropathy less than or equal to grade 1 * The participant must have an Eastern Cooperative Oncology Group (ECOG) score between 0 - 2 at screening * The participant must have a life expectancy of greater than 12 weeks * Ab…