This phase II trial tests the safety and side effects of glofitamab and obinutuzumab and how well they work in treating patients with mantle cell lymphoma that has come back after a period of improvement (relapsed) or that has not responded to previous treatment (refractory) after receiving CD19-directed chimeric antigen receptor (CAR) T-cell therapy. CAR T-cell therapy is a form of immunotherapy where the immune system cell, T-cell, is changed to attack cancer cells. Glofitamab is a bispecific antibody that can bind to two different antigens at the same time. Glofitamab binds to CD3, a protein found on T cells (a type of white blood cell), and CD20 a protein found on B cells (another type of white blood cell) and some lymphoma cells. This may help the immune system kill cancer cells. Obinutuzumab is a monoclonal antibody that may interfere with the ability of cancer cells to grow and spread. A monoclonal antibody is a type of protein that can bind to certain targets in the body, such as molecules that cause the body to make an immune response (antigens). Giving glofitamab and obinutuzumab may be safe, tolerable, and/or effective in treating patients with relapsed or refractory mantle cell lymphoma after receiving CD19-directed CAR T-cell therapy.