Exactly, those tiles are a mess anyway why are you trying to save them

And remove the small quartz backsplash, those are really only used when the walls are painted. Tile should come all the way to the top. Of course this is after you remove the existing tile.

"Can I install 3/4" pencil molding to sit on quartz backsplash and over tile to cover the gap? Will it adhere?"

Yes and yes. I'd cut it to fit, paint it, then adhere it in place with white latex caulk.

Don't follow KLUDGEY/"HOME JOE"....... with more kludge and Home Joe. Sorry, Joe Corlett, not everything should get a band aid fix. Sever the diseased appendage. Get the riser off the counter top, and re do the tile.

I shall only pray the counter tops were installed at level. Might want to check. If the old counters/riser were ripped off, FORMER AND ORIGINAL tile left in place? That is an entirely different story, and was a very, very bad idea. Conceived by.......someone.

No, Jan, the OP asked a fair question and I answered it. I don't assume to know his circumstances as almost everyone here seems to. Yes, it's not the best fix. Will it look much better and is it very inexpensive? You betcha.

Yes it's inexpensive. So is a 150 bucks worth of subway tile @Home depot, and grab a whatchamacallit on the way out to pop that riser.off the wall. : )

IF the poster could afford new tops as you said? That is the best solution. Which should come before the one where the OP says, "can't pay the mortgage, or feed my kids........what else can I do?"

Joe at your $200/hr rate and $900 minimum how is it cost effective. :):)

$100 a square quartz and .15 bathroom tile is very very far from a cohesive whole. Good design is a sum of the whole, but can only be as good as the worst component in the design. Better to have all medium or low cost elements that work well together than one splurge element that does nothing but make everything around it look sad.

OP, yes, you can add that pencil molding if that is what you want to do as Joe said; however, there are other options that might look better if you're up for it. Despite the combative tones of The Pros, they have valid points and suggestions to consider if you look past the attitude.

There is another less expensive option than getting rid of the the 4" quartz backsplash, taking off the old tile and re-doing with new (however cheap or expensive) that might suit your budget/inclination. You could take off the old tile, leave the 4" backsplash, smooth the wall with drywall mud, and paint. It's perfectly functional and will look fine.

You could also re-tile above that 4" backsplash. It's not my personal first choice, but you see it a lot, and again, if perfectly functional.

Lots of ignorant people here the OP asked a legitimate question if you dont want to answer it, keep your mouth shut. he doesnt need your criticism. only 1 guy answered his question we just did exactly what he said and it looks great see photos

something isn't level. if you have a gap variance that large - are the tiles differing heights? if you install the pencil trim will it then cover the tile and highlight different heights? or were the tiles all cut off differently / crooked? if the latter then good. If not - then your fix could accentuate the problem.