It is the lighter than the material on the tailgate, and storage compartment. They were attached with hot glue, or contact cement. The tailgate carpet is held on with hot glue. It is a PITA to get off, and usually damages the surface under it. If you heat it to remove it, it will probably warp the door panel, and that is not a good thing. The material is similar to the carpet, but thinner. If you are going to use heat, get a trial panel from the junk yard to practice on.
Do not use solvents on the lower door panels, they are polystyrene, and do not hold up well to solvents.
If you paint over the cloth on the doors with SEM, it will become stiff and nasty. There is nothing you can do to remove the SEM from the door once you have painted it.
Check with either a custom builder, or maybe a stereo shop. The often have specialty cloths to hide speakers.