Trim the old caulk with a utility knife, being careful not to scratch the finish on the tub or shower surround.
Use the putty knife to scrape out as much caulk as possible. Not all of the caulk will come out at this stage, but scrape out the majority of the caulk with the putty knife or paint scraper.
Apply a silicone caulk remover. The caulk remover may take several hours to work. Follow the manufacturer directions. Use the putty knife to remove the remaining silicone caulk. The caulk remover will make this step easier.
Use rubbing alcohol to clean the area. A mixture of one part chlorine and three parts water will also work. Scrub the area with the mixture and a toothbrush or bristled scrub brush. Rinse well when finished.
Wipe the area with a dry rag. Let the area dry completely before applying new caulk.