Hi, Frank,

If the removed tiles are all in one big rectangle....good. If not, I would remove enough tile so I had one single large area with four sides...all free of tiles.

Then prep the surface with a 4.5" angle grinder and a masonry grinding blade.....the old thinset will grind down quite easily....the concrete is quite hard. you should have no problem not grinding too deeply into the concrete. Now, you're all "set" for tile.

On my pool, I used a thinset made by Custom. It's the midpriced thinset at Home depot (about $12) and might be called "polyblend" but I can't remember for sure. It is a fine product.

I used Custom's (Home Depot) grout as well....I know it was called "polyblend" Very nice quality product.

You're gonna' make a mess....both grinding and installing. Go to whatever lengths you need to protect the rest of your pool from the dust, thinset and grout. Good Luck.