THose letters are standard whenever an initial grant of Unemployment Compensation is reversed after an appeal. If it has been determined to be a "nonfault" overpayment, then you cannot be compelled to repay, but the overpayment could be recouped from future benefits if you have another claim in the next few years. In over 20 years of practice I have yet to see a claimant voluntarily repay.
A fault overpayment, however, must be repaid. There can be criminal consequences for failure to do so. Fault overpayments usually result from some fraud on the part of the claimant, such as working and collecting UC at the same time.