4x4mm part fell out during battery replacement?

I replaced the battery following these instructions, and so far, so good. The only problem is that while I was replacing the battery a small part fell out: it is a very thin square about 4 mm x 4 mm with a circular hole in the middle, about 3 mm x 3 mm. I tried putting the phone together and using it without this part, and it seems to work, but I'd feel better if I understood what it was and could put it back where it goes.