The common thread in the first three readings is the difficulty of living a good life in a not-altogether-good world.
The framers of the lectionary are proceeding through both "Romans" and "Matthew" in order. They have matched the Old Testament and Psalm to "Romans" with the theme in mind. If there is a connection to the Gospel (the Syro-Phoenician woman), it is less obvious.
The Gospel is troublesome. Unless you are committed to Biblical inerrancy, you might conclude, as I have done, that the story is fiction. The First Evangelist's source for the story is the Second Gospel. Another Marcan passage (Mark 4:11-12) also presents Jesus as refusing the message of salvation to outsiders. Jesus supposedly spoke in parables so that his audience would not understand and thereby not have their sins forgiven. Since parables were a popular form for Rabbinic teaching, the presence of this obviously bogus passage in the Second Gospel satisfies me that it is not Simon Peter's authentic memoirs, period.
Let me suggest that the story was composed by a Christian during the early years, just post-Cornelius the Centurion, when there was a flap over whether to evangelize the non-Jewish world. As Jesus's followers, we settled the business quickly. Despite the attitudes of the time, we were faithful to the authentic spirit (and probably direct command: "Teach all nations") of our Lord.
The Bible mentions dogs several times. This is as close as we get to reading something nice about dogs. The faithful non-Jewish woman compares herself to a dog -- perhaps despised yet far more faithful than most humans.
E-Mail to: erf@kcumb.edu