If you carry comprehensive insurance on your policy, it will likely cover this kind of damage to the rental car (will have to check with your individual policy or agent to be sure, of course). You will have to pay your comprehensive deductible, which might be more than the damage, though! If you rented the car with a credit card, they may cover the damage as well or the part not covered by your primary insurance -- for example, they will cover the deductible, leaving you nothing out of pocket.
One thing I would check BEFORE calling your insurance company or telling the rental company is to call a local dealer for that car. Ask them if they have any touch-up paint in that exact color, which they will often give you for free. If the scratch isn't super deep into the metal or plastic, you may be able to repair the scratch so well that no one would ever know it was damaged. I think you just apply the paint, smooth it out, let it dry, buff, etc. Can't hurt to try, the damage is already done. Good luck.