Maybe I'm reading your comment backwards, starstorm, but if you scope the GSR you will have to raise your head in comparison to the iron sights.
Everyone's physical dimensions are different, yet the iron sights on my GSR align perfectly with my eye. A scope on the other hand, whether scout type or receiver mounted, both require me to raise my head a little bit. And that is with the lowest scope rings I have found.
So, I put a cheap Allen branded stock pouch/ammo holder on my GSR. The part that goes over the cheek rest of the stock raises my head almost perfectly for low mounted scope use.