I would probably just save up the money to replace it, rather than throwing any money at all to a partial fix.

On my monitor it already looks like a poor companion to the existing granite. Also I think the main backsplash tile is going to skew very peach, light flesh tone with grey wall paint.

Save your money till you can replace it. Painting the wall gray will only make it look worse.

It's fine and from the peek of your window, looks like it's a fit with the home style.

The tiles themselves are really pretty. You could post more photos to get suggestions for a new wall color. Gray and terra cotta can be mixed very succesfully but I think the grays tend to lean cool. Sherwin Williams offers color consultations and hopefully some other posters will chime in?

I wouldn't fixate on this aspect of the backsplash. It's not ugly, just not au courant. *shrugs* Better question is: how does it relate to the rest of the kitchen? As @barncatz noticed, the tile seems to fit the style of the house. That's a good thing. On my monitor, as @palimpsest pointed out, it's the colours that don't harmonize. Sometimes, it's a lighting issue that skews tones in a space (and in pictures). Pictures from further away and of the whole kitchen would help us give you better advice.

I would rethink the light gray tone paint.

Based on the very scant pictures you've shared, I'd instead look at a creamy off-white. Think adobe, southwestern, California mission.

Benjamin Moore Navajo White or Monterey White could be good color options.