I wouldn't pay grandparents for 'babysitting' but I would offer something to cover costs if they were providing regular childcare, which is different than occasional 'babysitting' (though my mum would never accept it).
My mum does not live close by (she lives in another country) and doesn't see our dd often as a result (we have no relationship anymore unfortunately with MIL, though this applies to her as well, back when we still saw her). When she does visit, she usually has our dd for at least an evening, sometimes overnight for us to go out to dinner or go away for a night. It is like maybe 4 times a year. No, we don't pay her and wouldn't even have thought of it to be honest! I think she would be offended at the suggestion! She doesn't see our dd much and is glad to stay with her (usually, we put her to bed anyway before we leave, so mostly it involves watching tv and taking herself to bed).
She doesn't provide any regular childcare though, by that I mean, like 3 full days a week while we work. We used a nursery (dd is now in school). If she did, she would similarly be offended by the suggestion that we pay her, but I would make sure that we at least provided her with things she needed, nappies, wipes, clothes, meals and snacks. Not so much because of the financial aspect, but just so it took some of the hassle out of her trying to work out and source things she needs. If we make sure she has everything then she doesn't have to worry about it herself.
I've honestly never heard of any grandparent being paid to babysit, but I could understand how offering something to someone who provides regular care so that parents can work would be reasonable. Seems a bit cheeky though to expect it for occasional times or for a quick afternoon when mum needs to go for a GP appt or something other than work, assuming it's not all the time.