To take or not take off the moldings

[MSGKUNERT]

I just took mine off of my 07 Denali and there is a thin (3/8") clear strip that still won't come off. I got the Eraser Wheel by Wonder Wheel and it still won't take it all the way off. Any ideas. Using my small dewalt drill and maybe thinking of hooking it up to the high speed drill.

 

[CTLT13]

That's one of the first things I did, take it off, looks cleaner without it.