Xbox Live stores any credit card you’ve ever used for purchases on the console, and there isn’t an interface on the Xbox 360 to remove them.
In order to remove the credit card from your account, you’ll need to login to the Xbox Live webiste:
http://www.xbox.com/en-US/live
Remember, this uses the Live ID you have tied to your Xbox Live account, not necessarily the email address you get notifications on. If you don’t remember the Live ID you used, go into Settings on your Xbox 360 and you’ll find it in there.
In the menu at the top, hover over My Xbox and select Accounts. This will take you to the My Account page.
Click on the Edit Payment Options link. Here you’ll see a list of all payment options you’ve used in the past. You can remove payment options, as long as they’re not tied to your Xbox Live subscription.
If you want to remove a credit card that’s tied to your Xbox Live subscription, you’ll need to first add a new payment option, or cancel your Xbox Live subscription.