SFGate

carolannr This laminate may have been installed with glue or countertop cement. First, I would try warming it with a hair drier to see if that loosens it at all. If it doesn't help any, you're going to have to use a pry bar at those loose places to peel it oiff, Regardless of how you get it off, there will be hard glue residue left behind - a real mess. There may also be some drywall damage. Don't forget to cut the caulking first. Since the "backsplash" was not a solid part with the countertop, it may be glued to the countertop too.

Laura Stermer warning: make sure you put a piece of scrap wood between the prybar and that drywall, or when you start pushing you make dents/holes in the drywall.

better to be safe than sorry..
It may not matter as you might end up scoring the drywall and removing to insert new drywall. make sure to find studs and cut drywall so that seams match up to the 1/2 point of the stud so you have room for those new drywall screws to grab into the studs.

fromny2nc Update: After considering all of your comments, I got cold feet about removing the backsplash. I figured with my luck, something would go terribly wrong. Then I was bored last night and tried one unnoticeable side to see if I could do it. Before I knew it, I had done the entire kitchen and with absolutely NO wall damage! Apparently, the original builder only caulked the bottom of the splash to the countertops so it was super easy! Thanks for all your information though, I definitely was not prepared for this job. Often projects seem easy until you get started.

carolannr You are so lucky but glad it came off so easily - it was obviously added as an afterthought so not really standard. Good luck with the rest of your plans!