Hi there @sassylady101 and thanks for posting on this forum. While I’m not an expert in bathroom repairs, I have removed and replaced old caulking in some old bathtubs before. In my experience, the best way to remove caulking would be to use a caulking removal tool. The tool I’ve used in the past is similar to [https://www.amazon.com/Homax-5860-2-Piece-Caulking-Smoother/dp/B000H5VX2W/ref=pd_sbs_60_t_1/132-4782453-4191343?_encoding=UTF8&pd_rd_i=B000H5VX2W&pd_rd_r=33e9d21f-f8a6-4215-b113-dd42a078dccf&pd_rd_w=AgGG7&pd_rd_wg=mtYL2&pf_rd_p=5cfcfe89-300f-47d2-b1ad-a4e27203a02a&pf_rd_r=M6HNZ7TGGFAPGKSX6HGE&psc=1&refRID=M6HNZ7TGGFAPGKSX6HGE|this one on Amazon]. I haven’t used any removers like Goo Gone before, but pairing a remover with the caulking removal tool may work out in your favor.
Let us know if there’s anything we can do to help. Good luck and happy fixing!
Justin Ogihara