@beanbag This sounds like the site is saving your data and not Brave. Have you checked your account or profile information on the site? Most will have a setting you can toggle to save (or not save) payment information. Some require the information be saved to use the application.
If you are not using any of Brave’s autofill features, then I think the payment application is saving your payment information, not Brave. I think you should check settings there.
Hope this helps. Please post an update. Take care. 