We always get those dissecant (sp? - silical gel) packets in the nori that we regularly buy. Can these packets be put inside sturdy 'aluminium' bags used to store tea eg. on top of the tea before closing the bag ?
I myself would be wary of putting it directly in contact with the tea, but there is really no evidence that food grade desiccants are harmful in any way or would change the flavor. I little empty tea bag filled with some salt or rice might do the trick too, though not for long term and I don't know if they might alter the character of the tea.