The piece above is the underside half of the pair of clips that sandwich the floor carpet. Maybe it is dislodged and stuck under the floor carpet somewhere.
The half that is stuck to your floor mat is the other (top) half of that pair - and belongs to the top of the floor carpet, not the mat.
I go in under the mat with the key blade, get it between the ring on the underside of the mat and the stud on top of the carpet beneath, and turn it through 90 degrees. Works every time for me.