In the pics it doesn't look so bad but in reality it was worse. Even worse if you compared with the rest of the phone, a pitty. The deterioration was only of the transparent coating, not the aluminium itself, fortunately.
Unfortunately, it seemed this cover wasn't very popular and there weren't many fake covers to buy for less money than the original one. This genuine one was 8€ without shipping, so almost half the price I paid for the phone. I had to fix this one.
You might think a good solution for these problems is sanding and re-coating, but it may be a bit aggressive for the first attempt of mending this. So I discover something that was worth a try.
What you need to start is a piece of copper to peel off the coating. Copper is less hard than aluminium, which means that there is no way you can scratch aluminium with copper. In Europe, coins of 1, 2 or 5 cents are great for this. So, let's start peeling.
When you're done, do a hard use of the eraser to clean the surface and to find if it is some coating you missed.
Almost finished. You can stop here if you want, the result is great and shiny. However, if you want to go further and have some car polish around (like this one or similar), it is good to use it.
Of course, it is almost impossible to photograph the difference, but this last photo includes the polishing. This step adds shiner and softer finish.
The end product is impressive. Now it's your turn.