If existing caulking line has toughen, it should be necessary to heat it up with a hair dryer until it becomes soft enough to scrape with blades.
2. Eliminate all existing caulking or grout from tub line at three walls.
3. Wash area with cleanser that contains bleach.
4. Make sure you remove all traces of old grout, caulking, mildew and soap.
5. Allow area to dry.
6. Apply masking tape to tile wall 1/4 inch higher above tub or shower. And to bathtub in the same manner as above. Do all three walls.
7. Practice a quality caulk like G. E. White Silicone Caulking for white tub, do not use clear.