Moved into a new house? Got a fancy new platinum card? Regardless, to update your credit card information simply go to the Account & Profile Settings page by clicking your name in the Profile menu at the top right of the rezora app.
On the Account & Profile Settings page, click on the View/Edit Billing Information link in the top-right box. That will take you to a page with your recent charges. There should be a button that says Update CC Info. Clicking that button will get you where you need to be.