I reserved LTT for dinner (characters should be there) and they didn't ask for a credit card number. They just asked my name and the number of people in my party. Maybe you need a credit card for Cinerella's Royal Table or something like that, though.
Now, Victoria & Albert's did ask for a credit card number, but I just checked my credit card bill online and they didn't charge it. I imagine if I fail to show at the date and time I reserved, they will charge it something, though. (There are other charges made on the credit card after the date I made the V&A reservation, so that's how I know they haven't charged it.)
-Dorothy (LadyZolt)