It sounds like part of the mechanism that raises or lowers the optical assembly and spindle motor inside the optical drive. (If it's like every other optical drive I've seen, the tray catches the plastic piece on the way in or out, and raises the assembly up or down when this plastic piece forced left or right).
If you can open the recorder and get inside the optical drive (apparently not difficult?), you can check for yourself. Maybe add a tiny bit of grease if it seems to stick; you should be able to manually open and close the tray a few times while the optical drive is opened to figure out which part needs a little help.