Green gets rebounds in his own "zone" at an acceptable rate. He doesn't crash the glass and get those outside his natural area very much. Doesn't really have a knack for it.
I'm actually kind of okay with Greens rebounding given the role that he plays. What bothers me a lot more is the lack of "hustle" plays he generates -- steals, blocks, tipped passes, etc -- and the fact that he really isn't much of a passer and only handles the ball if he's taking a few dribbles toward the rim.
That lack of versatility kind of requires him to be limited to his role as a pure complementary scorer with occasional mismatch-exploiting ability. He's a useful player, and he's actually more or less paid at fair value, he just doesn't fit on a rebuilding team with a lot of holes to fill.
The Celtics would probably do just as well with a cheap hustle guy that can shoot threes e.g. Demarre Carroll, simply because neither Green nor Carroll is gonna move the needle enough to get the Celtics into competitive territory.