Yes, it is legal: if an employee (whether full-time or part-time) makes a mistake and costs her employer money, the employer can ask her to repay it. If she refuses:1) They can terminate her, unless there is a written employment contract preventing them from terminating her in this situation or for this reason. They can do this regardless of why or how she committed the error, because without an employment contract, all employment is "employment at will."(Note: unless they agree in writing to not fire her for the error, legally, they could take her repayment *then* fire her anyway; it is simply less likely they will terminate her if she pays her error.)2) If they feel that she either was negligent (unreasonably careless) or deliberately caused the mistake and it's worth it to them, they could sue her; if they can prove she was at fault, they can get a court judgment ordering her to pay.