Is the money that the American government returned to the resident permissible, knowing that the reason for the increase in the amount provided is due to the submission of an incorrect application that was accepted by the government, and that the resident discovered the error after the amount was returned?

If the acceptance was with knowledge, then there is no harm in taking the amount. However, if it resulted from an error or fraud, then it is not permissible to take the excess, and it must be returned to the concerned party if possible without harm. Otherwise, the excess should be spent on charitable causes.