You do not need to peel the peaches. If they're very fuzzy, wash and wipe with a clean soft cloth. Leaving the peel on helps the peach to hold its shape once it's heated. You may find that the skin will loosen and may even be easy to remove just before serving if you'd like.
The secret to getting nice grill marks on peaches is to leave the peach halves in one spot on the grill. Resist the urge to move them around. Leave the lid of your grill open and grill for 4 - 5 minutes per side.