iPhone 7 Matte Black abrasion wear on the back and how to remove them

I am waiting my case to arrive and notice this happened on the back of my iPhone 7 matte black. I did my best to take pictures of them. It looks like abrasion wears than scratches. Anyone know tips how to fix this, like reapply the matte color on those wear lines, or if there is any service I can look for? I do not put my keys in same pocket and seeing this quite upset. They looks more obvious than in the pictures. Will toothpaste remove the matte black coating?