This phase II trial compares the effect of mosunetuzumab alone to mosunetuzumab with zanubrutinib or polatuzumab vedotin in patients with marginal zone lymphoma that has come back after a period of improvement (relapsed) or that does not respond to treatment (refractory). Mosunetuzumab 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). Zanubrutinib is in a class of medications called kinase inhibitors. It blocks a protein called BTK, which is present on B-cell (a type of white blood cells) cancers such as marginal zone lymphoma at abnormal levels. This may help keep cancer cells from growing and spreading. Polatuzumab vedotin is a monoclonal antibody, called polatuzumab, linked to a drug, called monomethyl auristatin E. Polatuzumab is a form of targeted therapy because it attaches to specific molecules (receptors) on the surface of cancer cells, known as CD79B receptors, and delivers monomethyl auristatin E to kill them. Giving mosunetuzumab alone or with zanubrutinib or polatuzumab vedotin may work well for treating relapsed or refractory marginal zone lymphoma.