Have old thin set on horsehair, how to begin a backsplash

Hi all, I removed tile backsplash in my kitchen and have old, wavy thin set on horsehair. I want to install a new backsplash, but I cannot remove the thin set without damaging the wall. I was thinking of putting up laminate drywall to cover it, then tiling over that. Any ideas on how to tackle this without removing the walls and replacing new drywall?