Any good quality teak cleaner should do the trick. Once clean however you need to oil the wood to prevent this from happening again. Here is a link from a marine store that offers advice on how to do this properly.
I have used the same cleaning and "brightening" products that I use on Ipe decking and furniture. Ipe is a dense tropical wood much like teak.
Penofins "cleaner" is a percarbonate based product which works a lot like the "oxygen" type cleaners. When cleaning wood this often imparts a grey color due to the reactions with woods natural tannins. It is recommended to follow up the "cleaner" with a "brightener". The brightener here is oxalic acid based and returns the woods pH back into a more normal range.
To maintain a "brown" wood like color a penetrating oil can be used. For those that like the natural grey color that ipe and teak weather into...you do not need to do anything.
A lot of manufactures say you should not oil teak or Ipe as it provides "food" for the mold or mildew...I say poo to that and oil mine as needed to maintain the warm wood look I like.
I have an Ipe deck and Ipe furniture that are close to 15 years old...in all of that time I have only have to "clean" it once so far. This cleaning happened a couple of years ago and the stuff still looks brand new.