Passing along credit card processing fees to customers

Hello all. I own own three veterinary clinics, two in Florida and one in Tennessee. We are about to open a second location in Tennessee, and we are changing our processing company up here. The company we are talking to is pushing us to pass along our processing fees to clients. It would just show up as a surcharge on invoices. I've been pretty against this as it feels cheap. But it would save me a massive amount of money. The Tennessee location will do about $900,000 this year, the overwhelming majority on credit cards and debit cards. So we would save 3% of that.

I'm not asking about the finances of it. Obviously it makes sense, it is a way to save tens of thousands of dollars. I'm asking about The ethics, optics, etc. Is it cheap ? Low class? It feels that way but I don't know if I'm saying this an objective light. I would love other small business owners input.