We find out how Jet lost his arm. The first reference to this was in episode number five, when Spike asks Jet what happened to his arm. This should be a clue to the viewer that we will soon discover what happened in Spike's past, but in the meantime, Jet is in the spotlight (literally).
The moral of this "musty old guy" story, is not to get involved in syndicates. Jet's partner was, and so was the assassin, and both of them died. In fact, Udai being disowned from his syndicate shows the fickle shift in leadership that can, and does, occur. Yet again a Bebop story correlates with the over-arching theme to avoid syndicates.