Restor. I-131 Upt. + Selpercatinib in RET F-P RAI-R TC

Inclusion Criteria: * Participants must have histologically- or cytologically-confirmed follicular-derived nonanaplastic thyroid cancer that is metastatic and/or unresectable AND harbors a known oncogenic RET gene fusion, performed in a Clinical Laboratory Improvement Amendments (CLIA)-certified or equivalently accredited diagnostic laboratory. * Tumor tissue or liquid biopsy-based next-generation sequencing (NGS), quantitative polymerase chain reaction (qPCR), and fluorescence in situ hybridization (FISH) for RET gene fusion detection will be permitted. * Participants ≥ 18 years of age must have measurable disease, per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1. \-- Participants 12 to \<18 years of age may enroll with either evaluable (i.e. anatomically visible tumor on cross sectional imaging, but tumors do not need to be \>1 cm) or measurable disease per RECIST v1.1. * Participants should have no single tumor deposit exceeding 4.0 cm in the greatest dimension. * Participants must have RAI-refractory disease, as defined by: * The malignant tissue does not concentrate RAI on a whole body scan following radioiodine administration * The tumor tissue has lost the ability to concentrate RAI on a whole body scan following radioiodine administration after previous evidence of uptake at any earlier timepoint, * RAI is taken up in some but not all tumor deposits on a whole body scan following radioiodine administration and/or * There is progressive disease per RECIST v1.1 despite RAI uptake on a whole body scan following radioiodine administration and/or * For patients 12 to \<18 years of age, there is persistent anatomically visible tumor on cross sectional imaging following prior therapeutic radioiodine administration * Participants may have received no more than a total cumulative RAI dose for treatment (not including RAI given for diagnostic purposes only) of 500 mCi (18.5 GBq). * Participants must have asymptomatic or minimally symptomatic disease, as judged by the treating investigator. For example, patients with bone metastasis associated with mild pain not requiring narcotics for pain control, or patients with lung metastasis associated with mild cough that does not limit the participant's activities, may be considered minimally symptomatic. If confirmation of this criterion is needed, discussion with the protocol chairperson is required prior to enrollment. * Prior external beam radiotherapy is allowed. For participants with disease limited to a prior radiotherapy field, this must be considered measurable per RECIST v1.1. * Participants may have had no more than one prior systemic therapy for RAI-refractory thyroid cancer, including lenvatinib, sorafenib, or other MKIs. This also includes chemotherapy and/or targeted therapy administered within a clinical trial, but does not include I-131 NaI or levothyroxine. Prior RET-specific kinase inhibitor therapy, such as selpercatinib and pralsetinib, is not allowed. * At least 28 days must have passed since any prior radiation or major surgery. At least 28 days must have passed since any prior systemic therapy for thyroid cancer, excluding thyroid hormone replacement. * Participants must be ≥18 years of age. Patients as young as 12 years of age will be allowed if permitted by local regulatory authorities and institutional review boards. \-- All patients of 12 to \< 18 years of age will be asked to provide assent and the legally designated representative will be asked to provide written consent. * Participants ≥ 16 years of age must have an Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1. Participants 12 to \<16 years of age must have a Lansky Performance Score of ≥ 60. * Participants must have a life expectancy greater than 12 months. * Participants must have the ability to swallow medications and have no gastrointestinal abnormality that may alter medication absorption. * Participants must have adequate organ and marrow function as defined below. Bloodwork must be collected within 7 days prior to Cycle 1 Day 1: * leukocytes ≥3,000/mcL * absolute neutrophil count (ANC) ≥1,500/mcL * platelets ≥100,000/mcL * hemoglobin ≥9 g/dL * total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) OR \<3.0 x institutional ULN for participants with Gilbert syndrome * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN OR ≤5 × institutional ULN if the liver has tumor involvement * creatinine ≤ institutional ULN OR creatinine clearance ≥30 mL/min * Participants must have serum potassium, calcium and magnesium levels within institutional range of normal (may be receiving supplements). Bloodwork must be collected within 7 days prior to Cycle 1 Day 1. * Known human immunodeficiency virus (HIV)-infected participants on effective anti- retroviral therapy with an undetectable viral load within 6 months are eligible for this trial. * For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Participants with treated brain metastases are eligible if the patient is asymptomatic AND follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression. * Participants 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. For example, participants with nonmelanoma skin cancer, carcinoma in situ of the cervix or malignancy diagnosed ≥2 years previously and not currently receiving anticancer treatment are eligible. Patients receiving adjuvant hormone therapy for breast or prostate cancer w