The myths of Thebes play an important part in Becoming Jason. They help contribute to the wider backdrop of Greece. But they also offer background to Heracles, who himself has come from Thebes. And the story of Oedipus offers another insight into the Delphic Oracle. Furthermore, Thebes is one of the kingdoms visited by Jason in his attempts to recruit heroes for the expedition and this gives an opportunity to contrast Thebes with other royal households and prefigure future events of Thebes in the coming generations.
The main myths of Thebes are well known: Laius' attempts to prevent the prophecy that he will die at his son's hands; his eventual murder by Oedipus who himself is trying to prevent a prophecy he has received; Oedipus' defeat of the Sphinx and acceptance of the throne of Thebes from the regent Creon; and Oedipus' subsequent marriage to his mother and eventual exile. Also mentioned in To Catch A Thief are the myths of Cadmus and Pentheus. Subsequent myths about the Seven Against Thebes and Epigoni expeditions are also touched upon obliquely in Becoming Jason and The Last Centaur. Thebes will almost certainly play a role in the rest of the saga.
I have also considered Thebes as a potential topic for a subsequent saga.