Instructions
Navigate to the official Xbox website (see Resources) and sign in with your Windows Live/Hotmail ID and password.
Click Marketplace at the top-right corner of your screen, above your avatar.
Click the "My Account" drop-down menu and select "Manage Payment Options".
Edit your credit card details or delete them completely by selecting "Remove" next to the card information.
Follow the instructions to complete the removal process. If you get the message "This payment option cannot be removed at this time. Go to the Payment method information page to view services associated with this payment option." you will need to either add a new payment option or cancel your Xbox Live Gold subscription.