Is there anything that can be done about the foam? I like this thing because of how good of shape it's in, and that's a pretty hideous blemish on an otherwise perfect machine.
You could disassemble the LCD assembly to reach the loose piece and then use an adhesive tape to hold it in place. Owing to the hassle of all the steps and (as @eyoungren experienced with a similar PowerBook design) the risk of inadvertently slicing my fingers, I’ve held off on doing this. Moreover, if I eventually do something like this (my 17-inch PowerBook, since posting this, also seems to have this piece moving about), it will be to do an upgrade on said PowerBook, not to the LED display on my A1261.