Great tip! I am going to try it.
I am guessing here, but it may be that the scratches are really 2 things- 1) slight buildup of oxidation from where the anodized finish was removed and 2) the underlying metal being exposed.
The Magic eraser will be great at removing the slight buildup of oxidation and whatnot. The shinier metal showing through the scratch may be partially filled and look less obvious by the minute amount of finish being buffed off.
total WAG though.