Black mould in silicon around tiles - spraying vinegar or tea tree oil enough or need to scrub?
I think you should remove all the silicone then use a bit of bleach to clean the area well to kill any remaining mold. Let it dry thoroughly and then put a new bead of silicone there.

You mention this is a rental property. You may want to talk with the landlord about this. If there is mold, then water is getting behind the silicone and potentially causing further damage. The owner should take it upon themselves to fix this.