I'd scrape off the rest of the old grout/thinset, slap on a layer of Zinsser Gardz and start tiling. It looks about the same as ours when we removed our old tile backsplash and I didn't have any adhesion problems after prepping it with Gardz.

Thank you for the tip! I'm going to do exactly that.

Zinsser Gardz is excellent. After scraping off the old thinset, apply the gardz then smooth the wall like ordinary drywall before tiling.

Hi everybody, I have a similar issue, but slightly different. The people that owned the house before us refaced the kitchen cabinets with RTF. They then also covered the sheet rock between the cabinets with the RTF and then installed the quartz countertops and backsplash over the RTF. I really want the RTF gone and we want to install glass tiles. Judging by the condition of the remaining sheet rock in the kitchen (there were several layers of wallpaper that they painted over between the wallpaper sandwich) I am certain whatever sheet rock remains behind the RTF, is in horrendous condition or will be by the time I cut and pry the RTF off which I am sure was affixed to the wall with construction adhesive. I came to this post because I was considering putting 1/4" cement board over the RTF and then tiling. The area is only about 1' high by 10' long. My other option is to sand the RTF and use Zinsser Gardz and then tile. The glass tile is small and lightweight and comes on sheets.

Just remove the drywall and all the layers. And put up new drywall.