Non-covalent BTK Inhibitor Nemtabrutinib in Combination With the CD20 Monoclonal Antibody Rituximab for the Treatment of Marginal Zone Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Diagnosis of MZL including splenic marginal zone lymphoma (SMZL), extra nodal marginal zone lymphoma (ENMZL) and nodal marginal zone lymphoma (NMZL), established by histologic assessment * Requiring treatment for MZL. Patients receiving prior systemic therapy as well as treatment naïve patients are eligible * Local radiotherapy not exceeding a total dose of 20 Gy at least 2 weeks prior the first dose of study therapy is allowed * Radiographically measurable lymphadenopathy or extra nodal lymphoid malignancy (as defined by Lugano Classification for non-Hodgkin lymphoma \[NHL\]) * Subjects with splenic MZL who do not meet the radiographically measurable disease criteria described herein are eligible for participation provided that bone marrow infiltration of MZL is histologically confirmed * Subjects with skin extranodal marginal zone lymphoma (EMZL) who do not meet the radiographically measurable disease criteria described herein are eligible provided that skin lesion measures ≥ 1.5 cm in diameter and is documented by photo or there are multiple skin lesions measuring \> 1cm in diameter on the body that cannot be incorporated in one radiation field and at least one of them is histologically confirmed as MZL * Subjects with gastric extra nodal MZL histologically confirmed and need therapy but do not have measurable disease and in which response to treatment can be assess by multiple random gastric biopsies * Subjects with conjunctival EMZL who do not meet the radiographically measurable disease criteria described herein are eligible provided that conjunctival lesion measures ≥ 1 cm in diameter and is documented by photo or there are multiple conjunctival lesions measuring together \> 1 5cm that cannot be treated by radiation because of previous radiation therapy, contraindications to radiation and patient refusal to receive radiation therapy. At least one of these lesions needs be histologically confirmed as MZL * Willing to provide a lymph node or tissue biopsy from the most recent available archival tissue or undergo an incisional or excisional lymph node or tissue biopsy * Subjects with splenic MZL who do not have a tumor to biopsy or an archival tumor tissue sample are eligible provided subject is willing to undergo a bone marrow biopsy or provide an archival bone marrow biopsy that was obtained before the date of the first dose of study treatment; bone marrow sample must show histologically confirmed infiltration of MZL * At least one of the following criteria for treatment initiation: * Involvement of ≥ 3 nodal sites, each with diameter of ≥ 3 cm * Any nodal or extra nodal tumor mass with a diameter of ≥ 5 cm * B symptoms (fever ≥ 38 degrees Celsius of unclear etiology, night sweats, weight loss \> 10% within the prior 6 months) or other symptoms attributed to disease or specific organ involvement associated with the relapse * Risk of local compressive symptoms that may result in organ compromise * Splenomegaly or splenic lesion without splenomegaly * Leukopenia attributed to MZL (leukocytes \< 1000/mm\^3) * Leukemia (\> 5,000 lymphoma cells/mm\^3) * Threatened organ function, especially for extra nodal MZL * Requirement for transfusion or growth factor support attributed to lymphoma * Involvement of 2 or more extra nodal sites, with tumor/lesion in each extra nodal site ≥ 1 cm * Progression or relapsed within 24 months after MZL diagnosis in patients previously treated with ≥ 1 line of systemic therapy * Life expectancy \> 3 months * Prior adverse events (AEs) must be resolved to grade 1 * Without bone marrow involvement: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * With bone marrow involvement: ANC ≥ 500/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Platelets ≥ 50,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement. * With bone marrow involvement: Platelets ≥ 30,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement. * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * Subjects with documented history of Gilbert's syndrome and in whom total bilirubin elevations are accompanied by elevated indirect bilirubin are eligible * Hemoglobin ≥ 8.0 g/dL * Aspartate aminotransferase (AST) ≤ 2.5 x ULN or ≤ 5 x ULN in the presence of liver involvement by lymphoma * Alanine aminotransferase (ALT) ≤ 2.5 x ULN or ≤ 5 x ULN in the presence of liver involvement by lymphoma * Creatinine clearance of ≥ 45 mL/min/1.73 m\^2 using the Modification of Diet in Renal Disease formula OR ≥ 45 mL/min by the Cockcroft-Gault formula * Seronegative for hepatitis C virus (HCV), hepatitis B virus (HBV) (surface antigen negative) OR * If seropositive for HBV or HCV, nucleic acid quantitation must be performed. Viral load must be undetectable. Patients with occult or prior HBV infection (defined as negative hepatitis B virus surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) may be included if HBV deoxyribonucleic acid (DNA) is undetectable, if they are willing to undergo DNA testing on day 1 of every cycle and every three months for at least 12 months after the last cycle of study treatment * Participants with HIV are eligible if they meet ALL the following: * CD4 count \> 350 cells/µL at screening * The HIV viral load is below the detectable level