The edge caulking is a shitty job and I hated it so much I have only done some areas on my boat so far.
I've cut along the caulking/teak edge with a stanley knife, then slid a putty knife along the caulk/gelcoat edge trying not to scratch the gelcoat too much. Then you can pry off a length.
Clean up, mask both edges, goop in new caulking (pick a more UV resistant one than Bavaria did) and flatten the goop with your finger. Remove masking tape immediately, before caulk cures. Keep some builders "wonder wipes" ready for if (haha, when) you make a mess, and a big bin and lots of paper towels. Also a choice selection of curses!
Good luck!