Is the floor tile to remain.. its traditional in style. just a subway tile for the splash but you could insert a solid color. i would want a more resilient floor as first thing to do.

Floor is here to stay until we do a full remodel. Then I will be doing hardwood on all floors

I would replace it. Something in a solid color.

What bothers me more than the backsplash is the wall paint. What I would do before any other change is paint the walls to a color that better coordinates with your floors -- I find the boys' bedroom blue to be quite jarring and it doesn't go with anything in the room. If you change the wall paint to an easier to work with pleasing color, it will open up more possibilities for backsplash color-wise.

FWIW, I like your floors. You have a lot of potential to make this a very attractive space with the combination of floors and cabinets you have now.....IF you ditch that wall paint. A soft creamy white for the walls and a backsplash in a coordinating green color would be beautiful IMO. Or if you want colored walls, some sort of light soft green that is tonally the same as the floors. So much potential here...

Agree that I'd get rid of the blue, then reassess. The backsplash doesn't bother me. It goes very well with the cabinets and the floor, and adds a bit of needed personality. If you get rid of it before replacing the floors, then the floors will be the bossy part of the kitchen.

For wall paint, I'd be looking at a green. Probably a less saturated version of the green in the backsplash. The problem with white/cream is that it can be difficult to get various shades of white to play well together, and there are already two of them in this kitchen (cabinets and countertops)