Instructions
Go to Xbox.com, and click the "Sign in" text link in the upper right corner of the website. This directs you to a Windows Live sign-in page. Every Xbox Live member created a Windows Live ID when they signed up for the service.
Enter your Windows Live ID username and password in the respective text boxes then sign in. Signing in directs you back to Xbox.com
Click your gamertag text link near the upper right corner of the website. This opens a summary page of your gamertag details.
Click the "Contact Information" text link, which is located directly to the right of your avatar.
Click the "Manage Payment Options" link on the left side of the page. The resulting page allows you to view and edit your credit cards.
Click "Remove" next to the credit card you wish to delete from your Xbox Live account. A dialogue window will appear.
Select "Yes" in the resulting dialogue window to delete the credit card.