I have a piece of plastic door molding on the lower back doors.

what is it for and can it be removed?

pic:

 

It can be removed, but it is there to help protect the paint, from sandblasting. Chevy switched to a clear 3M type of coating to place there on the 07 and up models.
Generally they are found on HHRs w/o running boards, but some who have added the boards have left those in place.

 

They must have switched mid-year or something because I've seen 07's with that molding.