Habaki has only a month to find Anotsu, before having to commit seppuku. So the matter will be settled in a month, possibly less. Also, Hanabusa told Anotsu to get away from Edo in a week, so the actual time for Habaki is even less (he cannot get out from the city since he's basically a criminal, as of now).
sure, since Anotsu's kidnapped Hanabusa, their "pact" could be considered void. But i think Habaki wants to settle the score right away.