How can I remove scratches from mat plastic?
its kind or hard to tell from the photo, but this looks like haircell finish, not matte.  its best identified by little swirly bumps, and is a really common finish on many plastic products (ironically for its ability to hide scratches).

if its haircell, there is not real way to remove it short of hours and hours of mechanical burnishing with burnishing rifflers, and they will cost you a fortune if you don't own them already.  you also have to be able to actually do the work, and its an art form. 

if its matte finish plastic, the best compromise will be sand the area smooth, and then to about an .25 micron finish (approx 400 grit wetsand).  then tape off the whole area and beadblast with glass bead.  you will have to experiment with different blasting media to get the finish you want.

either way, its probably cheaper to just replace the piece altogether, or have a new one fabricated.