In response to the OP, I think it can be a bit of a minefield. If the grandparents are doing full-time childcare then I think the parents should pay for meals and/or entertainment at least, but the idea of a fee seems wrong. That said, I don't think grandparents should feel obliged to help out.
My mum works full time, so she hasn't been able to help with either sprog, and to be fair it's not really her sort of thing anyway so I only ask her for babysits occasionally.
I've just gone back to work after having DS2, and DP's mother had repeatedly been saying how she would have him one afternoon a week, save us some money, spend some time with him, help out, etc etc etc. It was a kind offer and we didn't want to hurt her feelings, so we accepted and she picks him up from nursery for us once a week.
Things are already getting strained, for the sake of four hours' childcare that would only cost an extra tenner anyway. But I don't want to take it away from her, so I'll try and smile through it - it's not forever.