Beadboard in sheets - cut it to fit. Paint it some other colour.

This stuff is paintable - we used it in the galley of our boat. It took paint very well. You could use 'scrubbable' kitchen paint, to make it easier to wipe clean.

Here is a link that might be useful: Home Depot Beadboard sheets

Great idea, sara! My sister put up a beadboard backsplash when she was getting her house ready to put on the market. I was really surpised at how good it looked. I don't know that it would be my first choice for the long-term, but it would be excellent for the OP's application, and inexpensive, too!

The thing is you're going to remove what's there anyway. Just imagine how fabulous it would be to be rid of it altogether. If the tile was installed properly you might want to cut the sheetrock out and replace it with a new piece that you can paint temporarily. If the tile was installed badly (I'm guessing this is a real possibility) it can be SO easy to pull down. Why cover it when you can remove it (either way) in 1/2 a day max?

You can paint it. You clean the bejabbers out if it. Rinse well, Let it dry completely; Paint one coat of white pigmented shellac. And follow up w/ coat of enamel in any color you please. The last time I did this I used BM oil-based Impervo, which I think you can still get in quarts in some places. Two coats did the trick. I had it up for at least five years. Normal care regarding cleaning. I was surprised at how well it stuck to the tile.

HTH

L..

Check out the link below, which discusses using faux-concrete covered boards to cover up a tile backsplash. I think the end result looks great!

Here is a link that might be useful: Food52 kitchen remodel