the original Nikon LCD Monitor Cover is design to protect your LCD when the camera is not in use, you should remove it when you are using the camera, many people just leave it there all the time, of course this will get scratched easier, if you detach and attach it very often, it will get lose and lost it easier.
thou the grass is quite resist to scratches, but the cost of replacing the glass is much higher than a good quality screen protector like GGS or Martin Field.
hence I keep the Nikon LCD Monitor Cover in the camera packaging box, replace it with Martin Field screen protector.