Cottonballs, bleach mixture for around bathtub caulking
This was on Hometalk within the past 2 weeks. Need this fix for my daughter's rental house.
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http://www.hometalk.com/diy/clean/bathroom/how-to-get-rid-of-black-mold-in-your-shower-caulking-30392828
How to Get Rid of Black Mold in Your Shower Caulking
if you want you could also try a Clorox bleach pen.
Just place cotton balls or cotton rope on moldy areas and add bleach or vinegar. Let sit for a bit, then clean as normal.
Simply use original Clorox bleach.