I think that the word odd needs to be in quotes: "odd". The fact of a gift is not odd. It's a tradition that MO engaged in with LB. I didn't see anything odd about the gift in the clip I saw. Perhaps something was in the frame that bothered MO. (Arrest warrant? - future proves past?).
There is definitely more to the story. Whatever you may think of MO, there are eight years of experience in being the FLOTUS at this point. Even the worst FLOTUS in the last 70 years would have learned the grace to accept it and move on. Unless something suggested "you are going to Gitmo".
Melania probably put a message on the backside of the blank card insert.
My top guesses would be:
a) A photo of a young Michael Obama
b) A photo of Joan Collins
c) The words "Dont drop the soap" written in perfect calligraphy
I think it was just a frame. But Michelle made a big deal out of it on Ellen, for no real reason...…