Go to a good tile showroom. Look at trim pieces (sometimes called listellos or rails). Bring your pics and a piece of the splash tile if possible. The folks there are experienced in solving problems. Do not go to Lowe’s, HD or similar.

Can you take a photo further back? Very hard to advise without seeing some context.

Here’s another photo for context

My suggestion is to clean out all the caulk and the tile. Buy a scribe tool and follow the contour of the stone on a piece or drywall. Cut out. It should fit the profile of the stone. Then straight cut it just to clear the stone and attach to the wall. That will give you a straight line to butt the backsplash tile against. It will be extremely hard to scribe the tile and cut to butt up against the stone.

Thanks. I actually like the backsplash more than the ledge stone (sorry,) And I think the two are kind of stuck together. Literally. I wonder if getting rid of that rubbery looking sealant would help. Pity they were so messy with it.

Whoever did the stone first did you a favor. How would you remove the old tile if the stone were added in front of it? Since you're removing the tile anyway, maybe try a heat gun to soften the caulk/sealer, or at least try a hair dryer, and try to pull and peel off as much as possible.

Maybe use a dremel tool with some type of sanding head, to try to polish/sand the gunk off of the stone and tile.