Following the cabin air filter thread (Acura TL 2004 to 2008 How to Replace Cabin Air Filter - Acurazine), I did the disassembly of the underside of the dash and glove box.

There's a "U" shape latch that the glove box latches to that was causing the rattle. It's actually more of a "squeal" or "squeak". After removing the glove box, I could see that this hardware was held in place by 3 screws.
One on either side of the "U", and a 3rd towards the back. It's the back one that's the culprit in my case.
From a bird's eye view, this would be a "Y" shape pattern for the screws. The furthest screw had un-threaded more than 1/4".
While I was in there, I removed each of the 3, one at a time and applied some marine grease and firmly torqued back into place.

I apologize for the lack of original photos, but I've modified the image from the air cabin filter thread to indicate where this was:


While replacing the filter, you should check these screws and vice versa. No reason to take stuff apart more than necessary.

 

Definitely useful information. A few months after purchasing my TL, I closed the glove box and it all fell apart and fell down. Turns out that this screw was loose and fell out as well. I put it back in and all together and no more rattles.

 

I had this rattle for a LONG time.
I had replaced the air filter and checked the screws but missed the third screw. Couple months back I find a screw laying on the passenger floor mat and wonder where the heck it had come from.
Low and behold I come across this thread, again, but actually read what you said about the third screw.
The screw was missing, so I grabbed the one I had found and it was the right one! Mystery solved.
Also threw a piece of paper in there as a gasket/rattle preventer if it would ever come loose again.
Kind of a ridiculous design if you ask me...
Thanks for making this post without it I may not have realized about the third screw!

Side

Front

 

I was also dealing with this rattle for so long. Mine had completely fallen out as well and the design makes it a constant tapper. Thanks so much for this. The new silver bolt is the new one I put in to tighten latch down.