What does the Bible say about the faith of a Gentile woman?

In Matthew 15:21-28, we see a significant encounter where a Gentile woman approaches Jesus, pleading for mercy for her demon-possessed daughter. Despite being initially ignored and told that He was sent only to the lost sheep of Israel, she does not waver. Instead, she acknowledges the truth of His words, referring to herself as a 'dog' yet believing that even dogs eat the crumbs that fall from their master's table. Jesus responds to her humility and faith by proclaiming that her faith is great, and her daughter is healed. This account emphasizes God's grace that transcends cultural and ethnic boundaries and honors the faith that recognizes its own unworthiness but clings to God for mercy.