How do I repair tiles around the tub?

If you can carefully remove the rest of the tile and clean it then you could re-use it. It sounds like the problem was that drywall was used instead of cement board. If you can't re-use the existing tile, there are a lot of economical tile that can be used.

You need to remove the drywall completely. Screw up cement board. Install tile with a ready mixed mastik and spacers, if needed. Group and seal.

Some tiles are self spacing. The photo is a shower done with that type tile with accent tile.

It’s going to get worse before it gets better, sorry. Re-using the tile will only work if the grout & mortar both come off without breaking the tiles. My success rate is about 50%.

Take off more of the adjacent tile, until they no longer pop off easily, as the damage goes deeper than meets the eye.

If you really have drywall under there, then that’s got to come out, down to the studs. Inspect the studs for wood rot. If you’ve wood rot, lmk.

At this point, how little is left that’s not rotten underneath? It will be later, if it isn’t now, sorry, again.

One could either use purple drywall & coated screws and synthetic mastic w/ high polymer grout, sealed like crazy

or one could use a Hardibacker board with water barrier underneath.

or one could punt and put up a plastic panel like fiberglass reinforced plastic or bathtub panels.

tile work in wet areas is worth doing right, as you can see.

Let is know how bad the damage really is, and sorry once again, you really must remove a lot of it because the damage is going to get worse over time.

Thanks I will keep you posted!