What should I do about a gap between a quartz countertop and backsplash?
Did the countertop installers also install the backsplash? If so call them back and have them correct the issue. That seam should be sealed for appearance and to prevent any water from getting in there.

If the backsplash was already there it could be that they did a poor job leveling that section of countertop or the backsplash wasn't level.

Either way, call them in to look at it and correct it. Might just need to run a bead of caulk and they'll have the right color to work with the stone you selected.