I have similar. It's more of a constant grabbing, but it is constant and I basically get repeatedly scratched. Could you stop and say "no" while catching her hand? Don't know if it would work but that is one of the suggestions for if we get bitten, so you can see my logic....!
Totally sympathise! DS used to do this (now he pushes my chin to make my head turn...sharply sometimes!). I used to hold his hand, but he too got cross. I'd say that it's a phase - DS also used to push at me very hard when he was nursing (whilst still latched on - OWWW!), but he seems to have stopped that (fingers crossed).
Can you give her a soft toy or a muslin to hold while she nurses?