He can only sufficiently tell her what he's looking for in terms of blackmail and bribes for a few people. A wayward son, a matter of honor, old debts, ill-advised mistresses... Figuring out who reports to who, especially at the high levels of the Fire Nation military, might be more straightforward?
He can describe what industry and prisons and fortifications would look like. He knows a few sites that are probably industrial or prisons and wants, like, layouts or blueprints or guard schedules for those places if possible. He knows there's a Fire Nation supply base somewhere on this chain of islands and wants to know exactly where and what's in it, and how many ships there are, and how many men, and things like that. And this here is the Fire Nation's national symbol, anything with this on it bigger than a foot across he probably wants to know about. Chains and cages works for identifying prisons, too.
Yes, that would be good enough for the Pai Sho tiles. Especially if she happens to see them use it in a game. And there are a lot of words that can describe subtle differences in tea leaves, apparently.