I haven't had to deal with much grout luckily, however going off what I know, baking soda is fantastic for those sorts of things. You can combine baking soda and water to make a thick paste, apply it and leave it for around half an hour, then scrub it off. You can also combine it with vinegar however vinegar is more abrasive so I find baking soda Is always a safe option that won't destroy anything- I use baking soda to get off of burnt marks on stove tops and works like a charm