In these words is given us a pattern of catechizing and baptizing children; for the woman says not ‘Heal my daughter,’ or ‘Help her,’ but, “Have mercy upon me, and help me.” Thus there has come down in the Church the practice that the faithful are sponsors to God for their young children, before they have attained such age and reason that they can themselves make any pledge to God. So that as by this woman’s faith her daughter was healed, so by the faith of Catholics of mature age their sins might be forgiven to infants.
Allegorically; This woman figures the Holy Church gathered out of the Gentiles. The Lord leaves the Scribes and Pharisees, and comes into the parts of Tyre and Sidon; this figures His leaving the Jews and going over to the Gentiles. This woman came out of her own country, because the Holy Church departed from former errors and sins.
Reproduced in full. Translation: Oxford 1841 (Newman), public domain (Public domain).