Brentuximab Vedotin and Pembrolizumab in Treating Patients With Recurrent Peripheral T-Cell Lymphoma

Inclusion Criteria: * Patients must have a histologically-confirmed diagnosis of CD30- positive/expressing peripheral T-cell lymphoma (PTCL). NOTE: All PTCL subtypes are eligible, except for adult T-cell leukemia/Lymphoma (ATLL) and cutaneous T-cell lymphoma (CTCL); ATLL and CTCL are excluded per exclusion criterion below. Examples of eligible subtypes include but are not limited to the following: * AITL: Angioimmunoblastic T-cell lymphoma * EATL: Enteropathy-associated T-cell lymphoma * ENKTL: Extranodal Natural Killer/T-cell Lymphoma * FTCL: Follicular T-cell lymphoma * HSTCL: Hepatosplenic T-cell lymphoma * PTCL-NOS: Peripheral T-cell lymphoma, not otherwise specified * PTCL-TFH: Nodal peripheral T-cell lymphoma with T-follicular helper phenotype * SPTCL: Subcutaneous Panniculitis-like T-cell Lymphoma * ALCL: Anaplastic Large Cell Lymphoma NOTE: CD30-positivity is defined as \>= 1% of cells expressing CD30 as detected by immunohistochemistry (IHC) and determined by local review. * Patients must have received at least one prior line of systemic therapy and must have relapsed disease or secondary refractory disease meeting one of the below criteria: * Disease that relapsed within \> 6 months after completion of frontline therapy; or * Disease that relapsed within any time after completion of secondary/subsequent lines of therapy; or * Disease that was refractory to secondary/subsequent lines of therapy NOTE: Patients who have primary relapsed/refra…