How much gravel to remove to plant grass?
If you're collecting the gravel to reuse, get as much as practical.  If not, just leave it in place.  6" of topsoil should be more than enough for grass to establish itself, and the gravel won't hurt anything.  Soil will eventually fill in the gaps.  

You could speed the process by putting down a thin layer of cheap dirt or sand, and watering it to wash it into the stone, then put down the topsoil.  Or, you could mix the gravel into the topsoil when you put it down.

Until the stone is filled in and it becomes compacted, you will get more drainage than top soil over clay or compacted dirt, so water a little more often for the first season.