Odd drain cover. Was it existing? Perhaps it isn't adjustable for height.

Do you ever stand on this area? An un-flat floor is an annoyance.

Personally, I would try to find the same cover and just lay it on top of the exisiting so its flat... possibly longer screws if it being loose is a problem.

Sounds like a half-*** way of a fix, but the drain might not be adjustable and trying to fix that is not a walk in the park.

Looks fine to me.

A shower drain should have a lower collar at the waterproofing membrane level and a higher grid plate at the tile level that is adjustable in height (usually 1"+) so it can be set flush with the tile (not below or above it).

Ask the tile setter to raise the grid plate to where it is supposed to be even if it requires resetting some of the tile.

Is that grout stuck in the texture of the wall tile? Hope they are going to clean that off for you.

Yea there shouldn't be grout overtop of the drain cover. It should to be able to be taken off if needed.

Almost looks like a tile-over.

As the others have mentioned, you need to be able to remove the drain grate. If you can't remove the grate, then have the guy back to make the repair. I recommend talking about the repair before letting him make any dust.

What’s involved in raising that?

Don’t they usuall screw n and then get sealed with weatherproofing or thin set?