This phase II trial tests whether loncastuximab tesirine works to shrink tumors in patients with marginal zone lymphoma (MZL), a type of immune cell cancer, that has come back (relapsed) or become unresponsive to one or more treatments (refractory). Loncastuximab tesirine is composed of an antibody, called loncastuximab linked to a chemotherapy drug called tesirine. Loncastuximab attaches to specific proteins in the cancer cell and delivers tesirine only to the cancer cells because of this antibody. Ultimately this results in cancer cell death only without exposing normal cells to the tesirine.