A Study Comparing Two Immunotherapy Options for Human Papillomavirus Positive HPV-Positive Head and Neck Cancer After Treatment

Inclusion Criteria: * Patients must have history of histologically confirmed squamous cell carcinoma of the oropharynx. * Must be HPV positive; testing must be compliant with meeting any one or more of the following criteria: * p16 IHC positivity (p16 IHC interpretation to follow guidelines by Jordan and Lingen et al.37). * HPV PCR positivity. * HPV in situ hybridization (ISH) positivity. * Completed curative intent therapy. Acceptable curative intent therapies may include any combination of surgery, radiotherapy, and/or chemotherapy is eligible. Curative intent therapy must be completed at least 1 month prior to enrollment. * Any T or N stage at time of initial diagnosis is permitted, including patients with unknown primary, supraclavicular or mediastinal nodal involvement at the time of curative intent treatment. * Detectable ctHPVDNA in plasma confirmed by NavDx prior to enrollment based on the clinically validated circulating tumor-tissue-modified HPV (TTMV®) DNA plasma assay. Patients with detectable ctHPVDNA in plasma from other commercially available CLIA-certified assays are also eligible, however a positive NavDx assay is required and will be obtained during screening. * PD-L1 biomarker analysis from a core or excisional biopsy must be performed by IHC using the 22C3 antibody and a CPS score must be calculated for stratification. If unavailable, result from a fine-needle aspirate can also be acceptable. Local testing is acceptable. * No definitive clinical or radiographic evidence of disease evaluated by clinical examination and cross-sectional imaging and/or PET imaging prior to randomization. Patients with equivocal results on imaging are eligible. * Patients must be willing and able to provide written informed consent for the trial. * Patients must be at least 18 years of age on day of signing informed consent. * Have a performance status of 0 or 1 on the ECOG Performance Scale. An ECOG performance status of 2 is acceptable if the patient was ECOG 0/1 prior to curative intent therapy and is in the midst of recovery from curative intent therapy. * Demonstrate reasonable organ function as defined below in Table below * System and Laboratory Value * Hematological * Absolute neutrophil count (ANC): ≥1,500 /mcL * Platelets: ≥100,000 / mcL * Hemoglobin: ≥9 g/dL * Renal \- Serum creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl): ≤2.0 X upper limit of normal (ULN) OR ≥30 mL/min for subject with creatinine levels \> 2.0 X institutional ULN * Hepatic * Serum total bilirubin: ≤ 3 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 2 ULN AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better. * WOCBP must have a negative serum (beta-hCG) at screening. * WOCBP are defined as women who are fertile following menarche until becoming postmenopausal, unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy, and bilateral oophorectomy. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause. A high FSH level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single FSH measurement is insufficient to determine the occurrence of a postmenopausal state. The above definitions are according to the CTFG guidance. Pregnancy testing and contraception are not required for women with documented hysterectomy. * Male study participants with WOCBP partners are required to use condoms during the study and until 6 months after the last dose of study treatment unless they are vasectomized or practice sexual abstinence. * Vasectomized partner or vasectomized study participant must have received medical assessment of the surgical success. * Periodic abstinence (calendar, symptothermal, post-ovulation methods), withdrawal (coitus interruptus), spermicides only, and LAM are not acceptable methods of contraception. Female condom and male condom should not be used together. * WOCBP must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction during the entire trial and until 6 months after last treatment. * All men must agree not to donate sperm during the trial and for 6 months after receiving the last therapy dose. Exclusion Criteria: * Clinical or radiographic evidence of gross disease that warrants further curative intent therapy or systemic/palliative therapy (e.g. platinum containing chemotherapy, cetuximab, pembrolizumab). * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (\>10mg of prednisone equivalent) or any other form of immunosuppressive therapy within 14 days prior to the first dose of trial treatment. Physiologic replacement doses are allowed up to and including 10mg of prednisone/day or equivalent. Inhaled or topical steroids are permitted, if they are not for treatment of an autoimmune disorder * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1