I removed the grout using a chisel as a scraper. It worked pretty well. Labor intensive. Nowadays, they probably have a power tool that can do it faster.

Give one a try and see what you think.

But it was time consuming. I'm thinking an oscillating tool with the appropriate blade might be worth a shot to speed things up, but if you don't own one you will have to buy/rent one.

along with any grout along the edges. I'd use it but remember I'm cheap.

It is labor intensive and it is all about protecting the integrity of the glaze while getting rid of the adhesive.
You start with scraping tools to knock it off. You then go to abrasives which creates a lot of dust. The abrasive part means orbital sanders, angle grinder fitted with abrasive pads...packed with many pads behind the one you use.

It's a matter of using the most aggressive tool first and finding out you are chipping the part you want to keep, you go to less aggressive, to the point you are hand sanding to get rid of adhesive that may show. The back of the tile can be aggressive, but move your wrist with the power tool to leave ups and downs so that the restored tile will set forever.

If you take on this job, I guarantee you, that you will be an expert in this. Me...I'd sell it or toss it.

but it's more for taking out grout on tile that's installed