One approach would be to bump or build out the backsplash wall if that's at all possible (meaning, it won't interfere with anything else). You can either cover your existing sheetrock with another layer of sheetrock or, if you don't have to make-up too much add'l space, your tiler might be able to build up/out the wall with mud or thinset.

When we had our bathroom redone we had a very bad tiler and he left a gap between the floor tile and tub. We could have made him tear it all out and redo the floor, but instead we laid a row of thin pencil tile that matched the floor tile and tub. I can post a picture later when I'm at my home computer.

I love catmom's idea of building up the wall to create
the illusion of one piece of backsplash.
Or maybe you could have the quartz installed as backsplash.
like this....

The other ideas is to accept it as is. It can still be really pretty. Go with the short backsplash and just paint.

Full stone backsplash.

boxer - the second to last one is a great way to use an organic looking stone as a bs!

I think there may be quarter round tile to cover the gap and you can skip the small strip of quartz.
Of course, there is nothing wrong with the 4" strip. It is all up to personal preference. A 2" strip or 3" would also be just fine. I'd see how the tile lays out best because one of those sizes may give you fewer cut tiles. I'd ask the person who is installing your bs what size they'd prefer.

Thanks boxer, but I actually meant to build up the wall if she decides to forgo the 4" piece of quartz. If there is a gap at the back edge of her countertop it'll be narrower, or perhaps non-existent because of the extra thickness of drywall. Then she can just tile over this new wall, down to the counter.

Is this the way it's done when a 4" granite backsplash is added? I've seen several people post about removing the granite backsplash, which sound doable, but I haven't read that they may find the counters stop well short of the walls.

What would I do?

When I did a mini-redo of my old kitchen & got new countertops, I thought I would tile the BS. Pressed for time, I textured & painted it thinking I'd have time later to look for tile.

Ended up that I liked having a painted BS. I hang a few items there and change them out frequently. Sometimes, I take everything down & leave it undecorated for a while. Love how easy it is to change things up, esp. being someone who gets bored easily & who is always going to rummage sales & making new acquisitions.

I would wait to see how things look once the countertop is installed. If there aren't any significant gaps, you don't have anything to worry about and can do whatever you want - tile, or quartz to whatever height you want. If there are gaps you can decide how best to go from there. There's certainly nothing wrong with not having the backsplash decision made right away as many other GWers can attest to!

Keep the 4" backsplash as planned. There's absolutely nothing wrong with them, especially since you didn't think there was before visiting here. Many of the people here who talk them down are just chasing trends. Those pictures from Boxerpups show that they still look good when done well. We've all seen plenty of tile backsplashes that don't work too.

A good tiler can still hide many counter not-being-flush sins, up to about 3/4" if not a bit more. They can backbutter the tiles, that is, build up the mortar behind the tiles to compensate. Don't sweat about finding thicker tile!

But as others say, it's not a crime to have the short countertop-material backsplash, either. :-) Why don't you have them deliver it but not install it, until such time as you've decided whether you want it or not? It's really just a matter of using an epoxy glue and sticking the thing on, as long it's already measured etc.

Thanks, everybody, for the advice and the pictures!

After talking with the installer, we've decided to go with the 4" backsplash if it is necessary to compensate for any gaps. He felt that cutting it down to 2" would look funny, like it was put in there to cover up a mistake.

If we are lucky enough that the fit is tight without the backsplash we'll use the backsplash to make a bunch of coasters. :-)

Another update! The installers just left, and the fit was perfect so no backsplash was needed! The counters look beautiful and now I am even more excited about creating a tile backsplash to go with it.

And where are your photos? :)