I accidently backed into a concrete pillar in a parking lot. Fortunately I was accelerating so the damage is not that intense. Went to a body shop and they said that it looks like just the cover, and may be a bracket, which they don't repair but just replace. They said I might be able to clean it up myself instead of buying new bumper covers.

To me, it mostly look like some intense scratching. Does anyone have any suggestions on how to make this look better?

Bumper scratches

Bumper scratches close up

 

Because the bumper style is bare plastic with no paint, not much you can do.
You can probably lightly sand it to get rid of some of that white, but dont expect it to look original.

 

I would lightly sand it with very fine sandpaper to knock off the worst of the scratch and then employ the black bumper restoration trick using a heat gun. Youtube has videos of this. You probably have to do the whole plastic part to even it out.

 

The heat gun "trick", is a short lived fix. It fades back and in some cases is worse.