I just received the same car mount and was able to place the magnetic blade (without removing the adhesive tape) inside my TPU case. It's a little tricky to keep it centered while inserting the phone back in to the case, but I could keep a finger on the blade to keep it steady. Once the phone was fully back in the case, the blade hadn't move at all and it sticks to the mount perfectly without any movement or drops.
I also have a second blade on another case (applied on the back of the case), so that's another option. Buy a cheap case just for the car, but that could become tedious.
Edit: I have the blade vertically in place when the phone is in portrait view. Easier to hold the blade in place in landscape when putting the case back on.
Sent from my HTC One M8