The mold seems to be embedded into the grout. How do I get rid of it?
If you can find it, get Tilex Mildew... It will kill any mold and mildew and should bleach it clean if its not too far gone (or if you can't find it, try full strength bleach). If that fails you'll have to remove all the silicone (scrape it and then use a proper silicone remover to clean away ALL the residue - otherwise any new sealant will NOT stick) then re-caulk the area with a proper mold and mildew resistant caulking formulated for kitchen and bath (check the label).
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I've never had any success removing mold. Remove the grout and re-do it. Polyurethane sealants seem to be less prone to it. I used a marine seal called "Sikaflex" when I did mine.
Lysol, don't inhale spores.