That's... Actually quite the ingenuous idea. Not necessarily or strictly caligraphy, but if the favor is minor enough we can basically owe them little enough that it is not a problem either.
And if we *do* ever want to become temporary allies, well...
Small favors could add up over time into some sort of working relationship during the Winter Court, without forcing us to make a big move on the second or third day.
Remember, it's early in the Winter Court, and so for a Scorpion-like strategy, the worst thing we could do is commit ourselves and reveal ourselves too early.*
I wonder if we could bring the favor around to discuss Go? Like, 'To learn to become better at Go is [Philosophical stuff] and thus a good opponent to match against is a great favor?' Make this whole thing about Go in a way...and they can certainly draw conclusions.
They'll guess that we're going to participate in the Go stuff later on, if we say it right it shows respect for their skill even though they lost, and it 'tells' them that we're likely to use Go as a means of diplomacy in the future, if we're looking to gain skill at it.
Whether we want to or not.
Edit: Also, questions: how does training work? I mean, from what I can guess from the dice, they're better at Go than us, but we're smarter, is that right?
*Better to set the stage now and start making major moves later, after all. See how the pieces fall, etc, etc.
Edit 2: There's also a second message in asking for a small favor.
It implies that both US and the Clan don't NEED any favors. That we're strong (stronger than we are) and in control. If we asked for, I dunno, economic help, that implies that we NEED economic help. If we asked for a polo pony, it'd imply we (the character, not the clan) have some need for a polo pony.
So by asking for little, we're implying a strength that doesn't exist, which is a good thing! It's lying without some of the pesky problems that lying lead to, like being found out to be lying. Merely implying certain things has fewer of those traps.