You'll need to use a real small grade sandpaper.... we call it a zero grade emery paper down our side.
It's black in color and works well with water. It's used for bodywork of vehicles.
That ought to do the trick, you'll not need to go down all the way to the metal but you really need to match the shade of black to get the right look.
Wet that area and then sand it of the edges of the left paint on the case is going to get flakes , something you might not want.