Removing caulk from a bathtub can be a time-consuming, messy job. But it's one you can do yourself. Just make sure to set aside enough time.
Step 1 - Clean
Clean the bathtub thoroughly to get rid of existing soap scum and mold and let the bathtub dry completely.
Step 2 - Use a Putty Knife
Then, find an edge of the caulk that is already peeling and wedge a putty knife underneath it to remove the caulk. Take special care not to scratch the tub fixture when handling more stubborn pieces of caulk.
Step 3 - Use a Razor
Use a single-edge razor blade tool, like those used for painting, to slice caulk out of smaller spaces. Remove stubborn pieces of caulk from deep crevices with a pair of pliers and clean the remaining caulk away using a bristled scrub brush or hard toothbrush.