That is actually the internal diffuser for the apple logo that is between the backlight and the plastic apple logo itself. It's a round plastic disk that is normally adhered to the metal of the screen.
You would have to remove the lcd panel to get to it and then the backlight box. I would strongly recommend against it, as just touching the pages of the diffuser can cause permanent damage that will show up on your screen image. There are many more things that can go wrong than there are things that can go right with that job.
@salmonjapan has a decent answer, not the ideal solution, but if it is an eye sore, I would recommend something similar.
Sorry for the bad luck! But if you do attempt, take some good pictures and upload a walk through for us!