You would just call dining back. Some have reported luck in getting the credit over the phone and others have reported that dining told them they'd get the credit at the restaurant the day they ate there.
The policy may have changed since December, but at that time....
We made our ressies and they took our CC number but charged only $10 per person. When we went to the CRT lunch, they brought the bill showing the $10 per person deduction as already paid AND the 20% of total cost deducted for DDE. I added the tip, signed the ticket and the remainder was billed to my CC at that time.
I already had the card, but forgot to tell the CM when I was booking it. I called back a few days later (this was about a month and a half ago) and got a super nice CM who credited me back the money over the phone. I just called the 1-407-WDW-DINE to get it done.