Wow! That is very unique and EASY to look at......I like it!
I think what you have in your grout is some mold and perhaps algae.....doesn't really matter WHAT it is, just how to get rid of it.
I would take a spray bottle filled with 1/3 bleach and 2/3 water and simply go around the edge spraying that solution directly on the spot and then brushing with a deck brush.
That may not get it all so you could try some abrasive cleaner (like Comet) used sparingly. Last resort would be to apply muriatic acid but I think you will have most if not all of the stain removed before you need to try acid.