This is such a difficult question! I'm a mother of 2 young kids and this is what I would do:
It all depends on whether it's regular babysitting (like, more than once a week and requiring a regular ongoing commitment from her), or not.
If it's regular (e.g. as a form of childcare to allow you to go to work), then I would think you should pay her (or at the very least offer to - or arrange for some gift-in-kind instead). Since she is the grandmother of the young kids, I wouldn't think the amount paid need be as high as a professional daycare provider.
On the other hand, if the babysitting is not 'regular' (e.g it's just to allow you to attend social events occasionally; or it's 'backup' childcare for the odd day when the kids usual childcare is unavailable such as public holidays & you still have to work) then you really shouldn't be expected to pay her. Although a small gift like some home made muffins might be a nice gesture.
Hope this helps. Like I said it is a difficult question and I'm really eager to see what others have to say, especially the grandmothers.