How and what tools would I need to remove grout without damaging the tile backsplash and granite countertop. The cabinet has settled and crack appears on the whole length of the countertop was installed 10 yrs ago.
Since the grout has not broken and just has a crack, it would be more appropriate to add a thin bead of caulk over this section (silicone or matching latex).
You can take the grout out and regrout, however it will crack again.
I prefer grouting - and then caulking later after cracking - in these areas. The reason is with a larger gap you have to apply more caulk and it fails quicker and harder to maintain. It might seem like why grout and have it fail. Well because it takes 20 seconds to grout it and cracking isn't really a failure for a backsplash... more cosmetic.