This phase I/Ib trial studies the side effects and best dose of utomilumab and how well it works with CD8-positive T-lymphocyte (T-cell infusion) and aldesleukin in treating patients with ovarian cancer that has come back. Aldesleukin may stimulate white blood cells to kill ovarian cancer cells. Giving white blood cells (T-cells) that have been activated by a vaccine with aldesleukin may kill more tumor cells. Immunotherapy with utomilumab, may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Giving T-cell infusion with aldesleukin and utomilumab may work better in treating patients with ovarian cancer.