CLS panels can rattle for a couple of reasons. One is a simple resonance where the film gets excited at certain frequencies. It will sound fine until you hit a specific note then it sounds like a Kazoo. This is also dependent on how loud you play it. If it is loose damping tape, it will buzz at almost all frequencies and volume levels. If in fact the damping tape has come loose, and it sounds like it may have, our best bet is to remove it and replace it with new tape on the OUTSIDE of the panel. It will be on the backside so it will hardly be noticeable but it will still serve the same purpose. It indeed does serve a purpose. It dampens or limits the excursion of the foil. It can rattle like crazy without it.
Now for getting the tape out. It takes patience, good light and a steady hand. Don't try to do it after polishing off a pot of coffee.
You will do best if you can find a high quality pair of tweezers that have a curve or hook on the end. Try to gently reach inside and snag the very pointed end of the offending tape. Once you have a secure grip, use something like a Q-tip or dull pencil to reach inside the grid and unstick the remaining length of tape. Just give it a slight push in spots down the length of it until you can see that it is completely floating. As soon as the entire length is floating, start slowly and steadily pulling the tape out through the single hole with the tweezers. If the tape snaps, carefully get another purchase on it and continue pulling.
Usually you will see the adhesive powder up around the hole you are pulling from. Don't be concerned about that. It will clean up later.
After the entire length of tape is removed, re-install some 2 inch wide clear packing tape in roughly the same area and pattern as the previous tape served. That will probably take care of it.