A saved payment method can be edited or removed by entering the checkout at the club where you are making a purchase in the mobile app.
You do not need to make the actual purchase, but you do not need to enter the checkout as if you were buying something -> press the "Continue" button in the bottom.
Once the continue button us pressed, a sheet will appear where you can click Edit next to your saved payment method. This allows you to remove that saved card.
You can also click "New card", which allows you to add a new payment method which you can save for future purchases.