You need to tear out your old backsplash, prepare the area then by putting up tile board, and you should be good to go. If you don't already have tile there, you can apply directly to drywall.
Remove the old backsplash tiles and glue. Use spackling compound to smooth the surface. When the surface is dry use a serrated trowel apply tile adhesive and new tiles
cut the panels with scissors or a utility knife and mounted by using polyurethane construction adhesive or high-bond double side tape,then polish it, mounted easily with double-sided tape.