Looks like caulk to me, however, why are you installing a backsplash? You already have a backsplash. When that piece is put up around the top of countertops, it is a backsplash and installing another above that, just does not look nice. You may want to remove that entire 4"? piece, clean the wall good, make any repairs from the removal, and then install your backsplash, if you want another type.

To clarify, we want to install a tile backsplash. We never considered actually pulling off the quartz backsplash

Yes, the quartz has got to go please.

When you tile, place a continuous shim the thickness of your grout lines on the countertop. Install the tile on top of the shim and grout. Pull the shim and fill the gap with color matched silicone please.

Definitely pull off the 4” quartz backsplash first.

Thanks for the feedback everyone. Nobody had mentioned this to us so we were just going to tile up from the quartz backsplash, but I'm glad I learned this now before starting. Now to just get some help removing it without damaging the wall too much.

There may be some damage to the wall, but it also shouldn’t make any difference since it will be covered.

If you don't mind the look, there is NO reason to remove the quartz. It's just a style thing. It usually looks better without it.

(It's actually more functional to leave it as a beefy bumper, but few people are hard enough on their kitchens to benefit from that extra function.)

I expect this is a silicone caulk. Get a razor tool and carefully cut away the caulk.

It had better not be silicone; silicone isn't paintable.

That is not correct. Some silicone caulks are paintable and labeled as such.