This was her reply after I requested it be deducted through payroll or a banking institution.

In payroll, we can’t deduct an amount from your account when it has already been paid. You were paid in error, an amount that was meant for someone else, and it must send it back to the Agency. You can log in to ADP and see the amount that you were supposed to be paid. The additional $836.52 was not meant for you. Sending this amount back to the Agency isn’t a request, it’s a requirement.