Yes, and that's totally fine. That's part of doing business and stores already take that into account.

However, the web shop I work at pays a 3% processing fee on returned payments initiated by us. It just makes no sense.

I don't know who your current processor is, but if you have any real volume, get off Square/Stripe if that's where you are at. Their rates are awful for volume sellers.

Square approached us a few years back and could not comprehend why we weren't jumping at their offered 2.6% + $0.35... "but the AI!?!?" is all their sales people could come up with.

We're well below 2% + $0.20 per transaction for all cards (including AMEX, believe it or not). Square/Stripe and the rest are great for being Turn-Key for new businesses. But for anyone with real volume, they are a joke.