Besides, I honestly would be sort of annoyed that you insist on making your dissatisfaction with your credit card processor my problem as a customer. I have my own problems to worry about, don’t make my saving 1-4% on groceries vs. 2-3% cash back on my credit card another thing I have to deal with. I’ve stopped shopping at certain grocery stores over less.
This isn't that uncommon, quite a few places in Europe do this actually.
Usually there's a barrier at the parking lot entrance. You get a ticket when entering, which you then have to put in a machine when leaving. The machine calculates your fee based on how long your car was parked. Modern systems are far more automated and use license plate readers instead.
If it happens to be a store-owned parking that charges per hour, it's to prevent abuse from drivers going to other stores nearby if it's in downtown. Charging for parking outside your store in a less dense district is equal to putting up a sign that you don't want customers.
Aka... charge for parking? I mean? This is pretty common? I've always found it annoying that stores will validate parking for motorists but if I choose to take public transit or bikeshare, I don't get any corresponding debate.
Why not go even further? Itemize the marginal cost of maintaining your property's parking lot for those customers who visit your business by car? Charge customers a "store heating fee" in the winter? Customer support fee if they talk to anyone? Just as ridiculous. Processing credit cards is just one of many costs of doing business that you need to account for when you price your products.