Removing undercoating?

Whether it's worth removing depends on what you're trying to accomplish (restoration, repairs, mods, cosmetic). If it is in sound condition you can leave it.

I removed all and will replace some when I'm done with my project. Used a propane torch (to soften), putty knife, and Goof-Off for the residue. Many other solvents will work for the residue. The job pretty much sucks no matter how you do it.