Better Options for Drug Disposal Systems To Reduce Diversion Act of 2021 or the Better ODDS To Reduce Diversion Act of 2021 This bill modifies the authority of the Food and Drug Administration (FDA) to impose safe disposal requirements as part of a risk evaluation and mitigation strategy for a drug. Currently, the FDA may require that a drug be dispensed with a safe disposal packaging or safe disposal system that renders the drug nonretrievable. Under this bill, the FDA may impose such safe disposal requirements without regard to whether the drug is rendered nonretrievable.