The BEST product to use to remove plate scratches is 'Barkeeper's Friend' (can be found in your local hardware store.) Since it is somewhat abrasive, I suggest doing a test on the back of a plate first. To do the test patch, simply add a small amount of Barkeeper's Friend to a damp sponge and gently rub a small patch on the back of one plate.
Once it has been determined that the cleaner and sponge will not scratch the plates, apply a small amount of cleaner to a damp sponge and gently rub the utensil marks off of the plates. One application might not be enough to remove dark marks, but be patient and try rubbing them off a few times.
IF the test resulted in your plate being scratched, (usually happens with delicate china) use another product called, 'Bon Ami' with the same instructions.