7. Jesus went into exile to Tyre, where he had friends who gave him a warm welcome, Mark 3, 8; 7, 24. He lived incognito there. His followers who saw him as a prophet or the Messiah may have been reminded of the narration of the prophet Jonah who went into to exile instead of carrying out his mission, Jonah 1,3, see Paul in Acts 9,29s.
In Homer’s Odyssey and in Virgil’s Aeneid the hero is diverted from his mission by a beautiful woman (Od. 5,14ss Calypso, Aen. 4,296ss Dido). With this ancient poetry in mind I imagine that the appeal by the Syrophoenician for Jesus to help her was originally a romantic set-up before Mark replaced the love story with a miracle.