The tiles were fine, the wall underneath was not. Once the old units came out the backing coat was stained, soft and speckled with mould where moisture had been sitting behind the kitchen for years.
We hacked the affected plaster back to sound brickwork, treated the wall and let it dry, then applied a fresh backing coat and skim. Drag the slider to see the same wall on the same day, before and after. The homeowner painted it a week later and the new kitchen went in on top.