Snap Back Inaccurate SNAP Payments Act This bill requires states to recoup any overpayments of benefits made to Supplemental Nutrition Assistance Program (SNAP) recipients and adjusts the formula for determining a state's liability rate for overpayments. As background, the SNAP quality control system measures how accurately SNAP state agencies determine a household’s eligibility and benefit amount and determines overpayments of benefits and underpayments. States that have comparatively high payment error rates for two consecutive years are assessed a penalty (i.e., liability amount). The Food and Nutrition Service (FNS) must use a statutory formula to determine the liability amount. Under current law, FNS must set a tolerance level for excluding small payment errors (e.g., $54 or less in FY2023). This bill reduces the tolerance level for excluding small errors to $0 for FY2024 and each succeeding fiscal year. The bill also requires state agencies to recoup any overpayments of benefits made to SNAP beneficiaries. The bill adjusts the liability rate formula to reduce the state payment error rate based on the percentage of overpayments recouped by the state. Further, the bill increases the multiplier used in the formula to 25% (from 10%).