I have an easy solution to brighten old teak.
1/4 c baking soda
1/2 c ammonia
1 c vinegar
Note: the solution will create a lot of foam when you mix the vinegar with the baking soda.
I used a green scotch pad and a lot of fresh water and it removed all the gray stuff. It brought the teak back to its original wood and lightly sanded some rough parts. Then I used Semco instead of varnish to protect. It's not as pretty as varnish but we can walk all over it and not worry about damage.
I can send you a link to some pictures if you wish.