As for the chair, I cleaned it carefully, washed the fabric retainer belt, and put wood cover up oil on the blemishes. The tray was more of a challenge. It took two coats of stripper to remove the rest of the old finish, then Gary sanded it with three levels of sandpaper, then I oiled it with mineral oil as you would a wooden cutting board.
It doesn't look perfect, but it isn't too bad, and of course, baby looks cute as ever in it.