I don't know the best way to fix it, but I do know you don't want any chance of water leaking underneath. If you happen to have any steel reinforcing rods in your granite around your sink and they happen to get wet and expand, your granite could crack. That's an expensive repair, and it will never look the same again. That risk aside, any water leaking down from around your sink could hit your sink base cabinet and cause irreparable water damage to the wood. If it's not leaking right now, it might if you have a full sink of water one day or splashing and that joint isn't sealed. A countertop fabricator would know what to do, so maybe someone else will suggest what to do in further comments.

You do not go over caulk, especially if what is there is not 100% silicone. It will not adhere. You need to remove and clean extremely well the area.

There is no topical solution to your problem. The sink must be dropped and reinstalled.