To remove old outdoor caulking, use a heat gun if necessary to soften the caulking, then scrape it off using a putty knife or a razor blade. If there are any remaining pieces, dip a cloth into mineral spirits, place it onto the caulking and leaving it there for a few minutes. Finally, scrub the area again using the cloth to remove the last traces of the caulking.
Use an old toothbrush to get rid of caulking in difficult areas, such as corners and seams. Make sure to remove all the caulking completely, as you may not be able to apply new caulking if there are traces of old caulking still in place. Once all the caulking is gone, add 1/4 teaspoon of dish soap to 2 cups of warm water, apply the mixture to a clean cloth, and wipe the area that was covered in the mineral spirits. Use another cloth and some clean warm water to remove the dish soap. You can also use some denatured alcohol to clean the surface afterwards.
After removing all the caulking, apply new caulking using a caulking gun. Be sure to press the caulk into the seam using a wet paper towel after applying it to the surface. To protect the surrounding areas, cover them with masking tape before applying new caulking.