That carpet's really glued down to the panels. But there's a couple of ways to get it off.
I like to use steam to soften the glue, but unless you have a steamer you're stuck to holding the panel over a boiling kettle. That will work but it's not the most efficient & be ready to have your fingers steam-burnt a few times.
Another way is to use lighter fluid. The type for Zippo lighters. That's Naptha. Camp stove fuel. It will soften the glue.
Start by soaking that into a corner of the carpet. Wait a couple of minutes to let the fluid do it's bit. Not too long though. Naptha evaporates fairly quick. Use a putty knife to get under the edge of the carpet. As you lift, rip, tear the carpet off, keep applying the lighter fluid to where the carpet meets the door panel.
GM sure didn't want that stuff to come off, so be ready to spend a bit of time on this.
Some (most?) of these door panels had random staples hidden inside the nap of the carpet, so that'll add to the frustration, too.
Once the carpet is off, there will still be a fair amount of glue & chunks of the carpet left on the panel. You can go at that with the putty knife & some more lighter fluid. Pliers can be used to get the larger chunks off.
To get the panel totally smooth & clean, once the majority of all that is off, I go over the area with my mini-angle grinder & a red fiber disc.