Here is what the 1 Year Lectionary Summary for Lent 2 says:
Jacob wrestled with God; he would not let Him go until he received a blessing from Him (Gen. 32:22–32). So it was with the Canaanite woman. Though Jesus seemed to ignore and reject her, she continued to call upon His name and look to Him for help (Mt. 15:21–28). Even when the Lord called her a little dog, she held on to Him in faith and would not let Him wriggle out of His words: “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters' table.” This Gentile woman shows herself to be a true Israelite, who struggles with God and man in Christ and prevails. “O woman, great is your faith! Be it done for you as you desire” (Mt. 15:27–28). This is the sanctifying will of God (1 Thess. 4:1–7)--to test your faith in order that it may be refined and strengthened. For tribulation produces perseverance; perseverance, character; character, hope. And hope in Christ does not disappoint (Rom. 5:1–5).
I think what is said here is all true -- I just don't think that this is the main point of the Gospel Lesson. We end up viewing this text on its own - in the abstract, and what stands out most is how Jesus is seemingly cruel to this gal - and then we jump to the times when God doesn't immediately answer our prayers and is seemingly cruel to us.
But that's not the point of this area of Matthew. Chapter 15 begins with a big discussion on the Pharisees and their love of their own tradition. And Jesus' answer, which is true, offends the Pharisees. The good, Jewish boys take offense when they are told they aren't wonderful.
Then you have this Canaanite woman, one who is so low (in Jewish understanding) that the disciples don't even want to address her directly. The disciples give into their pride in their heritage and culture - they are blind and they despise her.
And then Jesus speaks a hard word of truth - you don't deserve anything from me because you are as lowly as a dog. And unlike the Pharisees who hear the truth and are offended, she hears the truth and confesses it - yes, I am a dog - but YOU are good.
If we are to understand Christ's passion, understand what we see this Lent - we must forgo our own pride, our own self worth, our own love of our own actions. Instead, we must confess that we are sinners for whom Christ died.
This isn't about how good Christians will be persistent in prayer - this is about how Christians will in faith believe what the Word of God says and trust solely in Christ. It's about the wretchedness of man and the goodness of Christ - not about how you can be a good little Christian.