On the 2009 and 2010 Vibes, the fuel door hinge is riveted on by two rivets. Just drill the rivets out to remove the fuel door and hinge. Check the salvage yards for a replacement.
I see that you are from the Twin Cities by your tag, did it rust out from all the salt in the winter? If parts of the inner fender rusted away where the hinge was mounted, then you are going to have to fabricate replacement pieces to replace the rusted away parts or yes, replace the whole rear fender which would properly not be worth the expense and time because if the car is that rusty, it can not be worth much.