A Vaccine Booster (GEO-CM04S1) for the Prevention of COVID-19 in Patients With Chronic Lymphocytic Leukemia

This phase II trial compares the effect of the GEO-CM04S1 vaccine with the current standard of care vaccine in preventing COVID-19 infections in patients with chronic lymphocytic leukemia (CLL). The GEO-CM04S1 vaccine uses a modified vaccinia virus (MVA) backbone that may be more effective at boosting COVID-19 immunity in patients with poor immune responses. MVA strongly induces T cell expansion (infection fighting blood cells) even in the background of a suppressed immune system, which is the case in the targeted CLL patient population. Using the GEO-CM04S1 vaccine may be more effective at preventing COVID-19 infection in patients diagnosed with CLL.

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Age: \>= 18 years * Eastern Cooperative Oncology Group (ECOG) =\< 1 * Histologically confirmed diagnosis of CLL according to World Health Organization (WHO) classification * Prior COVID-19 Vaccination (2 or more Pfizer or Moderna) with last injection \>= 3 months prior * Fully recovered from the acute toxic effects (except alopecia) to =\< Grade 1 to prior anti-cancer therapy * White Blood Cells (WBC) \>= 1,000/mm\^3 (To be performed within 14 days prior to Day 1 of protocol therapy) * Platelets \>= 50,000/mm\^3 (To be performed within 14 days prior to Day 1 of protocol therapy) * Total bilirubin =\< 1.5 X upper limit of normal (ULN) (unless has Gilbert's disease) (To be performed within 14 days prior to Day 1 of protocol therapy) * Aspartate aminotransferase (AST) =\< 2.5 x ULN (To be performed within 14 days prior to Day 1 of protocol therapy) * Alanine transaminase (ALT) =\< 2.5 x ULN (To be performed within 14 days prior to Day 1 of protocol therapy) * Creatinine clearance \ 1 year (women only) Exclusion Criteria: * Known current SARS CoV-2 infection * Prior Evusheld or other anti-SARS CoV-2 prophylaxis \< 2 weeks prior * Prior hematopoietic cell transplantation (HCT) or chimeric antigen receptor (CAR) T cell therapy within the previous year * Systemic corticosteroids required for chronic conditions at doses \> 0.5mg/kg/day prednisone equivalent within 7 days of enrollment * Intensive cytotoxic therapies, T-cell depleting therapies, within 30 days of enrollment; however, patients with stable disease on maintenance therapies are allowed (See ConMeds for lists of acceptable and contraindicated therapies) * Participants who have had a live vaccine =\< 30 days prior to administration of any dose of study vaccine or subjects who are =\< 2 weeks within administration of inactivated vaccines (e.g., influenza vaccine). Flu shots are allowed \> 2 weeks before a study vaccine injection and \> 2 weeks post study vaccine injection * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent (e.g., egg allergies) * Active infection not controlled on appropriate therapy * History of adverse event with a prior smallpox vaccination * History of pericarditis or myocarditis * Any MVA vaccine or poxvirus vaccine in the last 12 months * Females only: Pregnant or breastfeeding * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)