John Chrysostom

Yet nevertheless the woman was not perplexed, but on seeing her advocates prevail nothing, she made herself shameless with a goodly shamelessness. For whereas before this she had not ventured so much as to come in sight (for "she crieth," it is said, "after us"), when one might expect that she should rather depart further off in utter despair, at that very time she comes nearer, and worships, saying, "Lord, help me." What is this, O woman? Hast thou then greater confidence than the apostles? more abundant strength? …

Homily on the Gospel of Matthew 52 ↗

Theophylact of Ohrid

When the woman saw that her advocates, the apostles, had not succeeded, again she approaches fervently and calls upon the Lord.

Commentary on Matthew ↗

Jerome

But she came and worshiped him, saying: Lord, help me. He answered and said: It is not good to take the bread of the children and throw it to the dogs. The faith, patience, and humility of the Canaanite woman are preached in this remarkable passage. Faith, by which she believed that her daughter could be healed. Patience, by which she persevered in prayer even when rejected. Humility, by which she compared herself not to dogs, but to puppies. …

Commentary on Matthew ↗

Thomas Aquinas

But she came and adored him; hence she presses forward. And first her profession is presented; second, the response. Her profession is presented, because she recognized him as God, because she adored him. For although she had been repulsed by the apostles, she still pressed forward and adored. In this she recognizes God; Deut. 8:19: you shall adore the Lord your God, and him only shall you serve; Ps. 65:4: let all the earth adore you, O God etc. Help me. She does not say, pray for me, but, you help me, because you can; Ps. …

Commentary on Matthew ↗