That is glued to the actual door card, and is supposed to stay connected to the door card when you remove it to access the inside of the door (i.e. for repairing or lubricating the window track).
To remove the door card, you push down on that part (after unscrewing the door lock "nub") and you will be disconnecting about 5 or 6 clips that hold the door card in place under the chrome trim.
It's kind of tough to explain without pictures. Search for "e34 door card/panel removal DIY" and you'll see some detailed pictures.
If yours has become separated, I recommend taking it off completely and applying liquid nails to the back, and reapplying. Just make sure it's lined up right :thumbup:
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