Not the best & not the worst, either. A good bit of the problem is that there appears to be quite a lot of variation in the size of the tile.

Here are a couple more pictures.

Have you checked to see how flat the individual tiles are? Grab some leftover whole tiles and place them on top of each other, back to back. Then look for how much they are warped.

The overall job is on the rough side. But, when I see that much variation in the height of the tiles, then I have to suspect that there are a bunch of warped/ not flat tiles, too. These look like tile seconds. What is the brand? Where did you purchase them?

I imagine at this point there's nothing I can do about it?

You can chose to live with it or rip it out and replace. Or rip out & paint the backsplash.

Ceramic subway tiles require a flat surface and low notch trowel for the setting material, usually 3/16" or 1/4" v-notch or square notch to prevent shadowing. The adhesive will recommend the notch size and style. If the notch is too deep the setting material is too thick and the tile setter can't control the depth the tile is set at press-in. *This could be one issue with your tile. I suspect the trowel notch was too deep.

Most ceramic has built in notches and or a bevel to make all grout lines consistence in size and straight runs. When the tiles are butted together (no spaces required) or use a 1/16" spacer. *Your installer used no spacers and they could have cleaned the grout out better to make lines the same size.

My best guess why your tile is shadowing from overhead lighting is due to the subsurface was old and not super flat. Your backsplash isn't that bad. When we start a back-splash we either float out the subsurface to create a super flat surface or replace with new drywall and float flat before setting the tile. Some of the tiles can easily be removed and replaced to fix some of the issues that are bothering you. Call them back for some warranty work.

It doesn't look bad.

Thanks, everyone. We had the original walls torn out and new insulation and drywall, so the surface they were working with was new. The tiles were purchased at Home Depot. We're hiring the same company to work this summer on our bathroom (which will require more tiling), so it's good to know what I could ask them to fix and what to look for with the new work.

New surfaces on old studs can still be wavy and wonky. Super flat walls of the 200K kitchen installations on Houzz display have the crowns planed and the bows sistered, in order to get an actually flat and square surface. Your sub average 40K GC or sub average 1K tiler won’t do that for a backsplash.

For a standard 20K 3 piece hall bathroom, you have far more serious concerns, even though getting the walls flat and square is a concern. What waterproofing system are they proposing using?

https://www.ceramictilefoundation.org/homeowners-guide-to-hiring-qualified-tile-installer

https://www.remodeling.hw.net/cost-vs-value/2020/

I would think twice about tiles from a big box store. They are not the best quality. Purchase from a reputable tile store that will guarantee quality of their tiles.

I agree with Joseph Corlett.

They sort of remind me of handmade tiles.

if you didn’t point it out, I wonder how many would notice?

It looks good to me! Definitely not something I would tear out and redo. It seems better than most!

Whether in new construction or remodeling, it's important that the customer's expectations are aligned with the contractor's capability and what should reasonably be expected for the price level. "Friction" occurs when any one of those are misaligned.

A low-bid contractor using material from a big box store shouldn't be held to the same quality standard as a specialty contractor installing top-of-the-line materials. Nor should a specialty contractor produce something that looks like a DIY job.

I'm not a pro but I've seen much worse. This honestly isn't something I would worry about, and I'm someone that had to have my backsplash redone because the first job was terrible.

My tiles are from Floor and Decor and for the price I did not expect perfection. Before my tile guy started I actually went through the boxes and removed the wonkier tiles and asked that he used them only when necessary. He was a bit of a perfectionist and even took out some tiles that I thought were OK. He too started with new drywall as we had the old stuff cut out to make it easier but even with the new drywall, there are a couple of spots that aren't exactly perfect. And that's OK. Once you put your things back on the counters it will not be noticeable, and now I have to really study the backsplash to see where the slightly off tiles are.

Enjoy your remodel!