I would think you should be able to remove or update a credit card fairly easily. Circumstances change we may cut up or want to get rid of a card, they expire and need updating, or want to use a new card for all online purchases, etc. I always use PayPal here to buy items myself and within PayPal I have the option to add or remove cards. If you have a PayPal account maybe that could be a route.
I just looked on eBay because I haven't made any changes to my payment methods for ages and I couldn't even remember where it was. I'm not sure if you are using your phone or a computer but I always use a computer for anything major as I find there are more options and screens you can access. From the computer I found mine under My Account, Personal Information, Payment Info, Payment Options. I see mine there with a Delete Button, I would think that would be where you do it. Perhaps it is just asking you for a new credit card by default since most people removing a card would add a new one if they make purchases here.
You can close your account if you wish but I wouldn't panic because they have your credit card. They have had it for a while and you have been safe, they won't use it without you buying something, anything unauthorized your credit card company would remove anyways.
If it's just you don't want to use that card anymore for purchases I think you can change the payment method on checkout anyways.
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