Jesus was referring to the Jews as the children and the "dogs" as Gentiles. The lady seemed to see that what the Jews were rejecting (blessings from Jesus-or Jesus himself), would be beneficial to her and her need. What she was grateful for and wanted, the Jews didn't.
We asked ourselves these questions, "Do I appreciate all the blessings that Jesus has given me?" "Do I take advantage of opportunities that he gives me to share with others?" "When Jesus blesses us with a gift, do we take care of that gift or let it waste away in a sense and forget it's value to us?"
The challenge to ourselves and even those reading this would be how do we take care of our possessions? How do we appreciate our wives/husbands? Do I back out of opportunities to share because of fear of failure or I'm embarrassed? If we don't appreciate the blessings and opportunities God gives us, they may be given over to someone else. It's true with our possessions, marriages, opportunities and talents. Hmm, time for self-examination.