White cleaning vinegar will kill the spores. Check into wet & forget shower, unless it's a marble tub. It will slowly remove but more importantly if you use once a week it will prevent it.
We had to take out old grout and put in new. Bleach helped but mildew was under the grout so we to had to remove.
Hi Pat - This is the shower cleaner that we use to help keep grout and tiles clean and minimize the mildew - it works on kitchen grout too. Hope this helps! Hugs, Holly
PS - We have a FREE eBook with recipes for all of my homemade and all-natural cleaners. You can download it here --> https://pinkfortitude.com/thank#GreenClean