If the plastic is not coated-very deep and extensive damage can be buffed
out using a common electric hand drill and a buffing attachment ( like what
would be used to buff a car or table top).  Charge the fleece with  buffing
compounds of decreasing coarse levels (0ften you can buy a kit with three
grades) put on your safety glasses and have at it.  Finish up with a polish
intended for plasic.  It takes a while and makes a bit of a mess(bits of
the fleece come off) but the results should be good.