Rip it out or for go the tile, no to two backsplashes.

It is your kitchen, so do what you want and what you think looks good. I don't have a problem with it in theory. If you do, I would just suggest that you are careful about what you pair up together. The tile that you show it your picture does not appear to have the correct color to match your countertop to me.

Just rip it out. It’s held in place with a little silicone. More wasteful would be living with something you don’t like. If you do like it of course keep it.

I would just put something more behind the stove, and look for something other than subway since it will be a focal point.

I agree HU, regardless that tile sample would not do. Two very different tones. As of right now I think I will let the 4in be and if down the road I decide I want to tile it, I will be removing the lip, I like that look better from what I’ve researched.

If wasting the 4" is what is holding you back, see if you can't reuse the piece somewhere else. Shelf?

Take it out. Find a terrific tile for that area.

It doesn't appear that your top fabricator left the required inside radii on your cooktop cutout. I'd wrap the inside of the cutout with heat conductive tape and let it hang long. Run it on top of the deck too, set the appliance, and trim off any exposed tape. This is required on all solid surface (Corian) tops.

Do not use pans larger than the outline of the burner on the appliance please.

Really take the 4" piece off and get the tile you love .