I've heard of folks using
Oxygen Bleach Powder to clean and whiten caulk, but I've not tried it. Supposedly it's easier on the caulk than chlorine, and wont harm or strip the gelcoat surfaces adjacent to the caulk. Might try that, letting the oxy bleach solution sit wet on the caulk for several minutes before scrubbing, and then using an old toothbrush to scrub it clean.