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I think the title says it all but if needed - I'll edit this. Of course I googled but I got nowhere. Google results were total shit. Google won't help me if I don't know the exact name for that fucking thing. It's a very stupid design choice. Five regular old push buttons would be so much better.
About an hour ago I managed to stick it back on but I'm nearly 100% sure it's going to fall off again in week or two if not far sooner.
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Edit
I don't mean part of the unit itself. I mean just the thin plastic cover over the buttons that's ~3mm thick.
It's just buttons, in this case in a kind of soft silicone formed into one piece I'm guessing with extrusions on the other side to depress contacts? You can find similar things in some remotes and other devices. I would try and use superglue or an epoxy suitable for bonding plastic to other things and try drawing a thin line around the outside of it in a rectangle towards the edges. If you want to be extra careful you might try just gluing the thin sides and bottom of it to hold it in place without gluing the back.
As someone else said you can also just use clear tape, make sure it has a tiny bit of give but not enough to cause ridges or bubbles and you should have no issue using it behind something like clear packing tape.