With their new reservation system, I don't think they have full control over what it does or how it does it.
For example, I received this after releasing 3 of the 4 permits I had last year (I don't think I actually got the refund, but I'll check later):
You're all set! Your refund for Reservation #6-xxxxxxxx at Mt. Whitney has been processed and is on its way.
This email serves as confirmation that you’ll be receiving a refund for this reservation. Your refund details can be found below:
6-xxxxxxxx Original Paid:
$55.00 Total Refund:
Payment Type Amount Refunded
Legacy payment $34.00
Credit / debit card payments will be refunded to the card associated with your reservation, or you will receive a refund check in the mail with the address provided if you paid by cash or check (please allow up to 8 weeks).
Be on the lookout for your refund, and thank you for choosing Recreation.gov.
Either way, I think it's going to be a mess to sort out.