If it's the black unfinished plastic piece, i'm afraid the only way is to replace it since the texture is permanently damaged and to confirm your suspicion, it might discolor if you sand it and will affect the patern of the plastic.
The only way i can imagine trying to "repair" the marks would be to skillfully and patiently approach it with a plastic welding method , which would fill in the scratches/marks caused by the screws and even then, you'd have to ensure you choose the right type of plastic to weld(for proper bonding) with and see how you're going to match the final texture.
Long story short, it might need replacement since it may not be just superficial and it sounds to me like more of a permanent damage type of thing. As always, pictures help a lot in giving you a more accurate answer. Not sure it'd be worth replacing a whole bumper over a few screw scratches, might want to wait until it gets beat some more to really justify looking into that.