For this sort of application, clear silicone caulk is usually sufficient ... Start by removing as much caulk, sealant, and rubber as you can with a scraper or a razor blade.

When you're looking for a good silicone sealant to keep around for odd jobs, Gorilla Waterproof Caulk & Seal is our top pick. It seals out water, air and moisture for a mildew-free finish.