The only way i can think of is giving it a manual polish. Start with something like at least 1000 grain sanding paper. To finish it (after sanding away the deep scratches you can use some polishing paste like chrome polish. Even toothpaste will give a nice result.

Looks like they achieve the brushed aluminum look by using a thin film (with fine vertical stripes) over the back cover. If scratched it would not be fixed by polishing.

I am considering removing the film altogether. That would loose the brushed aluminum look (but it's scratched anyway) and leave just a metal back cover (which is fine).

The question now is - how to best remove this film?

i have done this using nothing more than wire wool and 1200 grade wet and dry paper