SNAP Second Chance Act of 2023 This bill limits the use of certain factors related to business integrity and reputation when determining the eligibility of retailers under the Supplemental Nutrition Assistance Program (SNAP). (The Food and Nutrition Service [FNS] must consider business integrity and reputation of the applicant under current law, and FNS regulations specify the factors that may be considered.) The bill limits the use of criminal violations to assess an applicant's business integrity and reputation so that (1) FNS may not deny a retail food store or wholesale food concern authorization to redeem SNAP benefits solely based on a criminal conviction, (2) FNS may only consider a criminal offense that has occurred within the past five years for the purpose of approving an application for authorization to redeem SNAP benefits, and (3) an applicant that is convicted of a criminal offense must not be denied authorization to redeem SNAP benefits on the basis of business integrity and reputation if the applicant establishes sufficient mitigation or rehabilitation. Sufficient mitigation or rehabilitation includes for financial fraud or deception, evidence that five years has elapsed since the felony conviction and compliance with all terms and conditions of probation or parole; for any other felony conviction, evidence that three years has elapsed since the conviction without a subsequent conviction of a crime and compliance with all terms and conditions of probation or parole; and other evidence of mitigation or rehabilitation and present fitness (e.g., the circumstances or social conditions surrounding the offense).