The woman who anointed Jesusí feet represents the Church, coming to Simon the Pharisee, whose house represents the synagogue. Simon the Pharisee is humiliated by the woman, whose lips are made holy by kissing Jesusí feet, and she is forgiven her sin. Jesus tells this parable to Simon as an act of reconciliation. What the woman receives from Jesus the physician in the forgiveness of her sins is miraculous healing that is equivalent to the miracles of healing Jesus did throughout Galilee (Ephrem).
She kisses Him on His feet because she believes He is the Son of God, just as the Church today exchanges a kiss of peace during the holy Qurbana so as to show publicly its faith and its confession by kissing Christ in kissing one another; Christ continues to be anointed with oil as the Church anoints the poor with the oil of charity (Ambrose).
It is the woman who confesses Jesus as God, and not Simon the Pharisee who sees Him only as a man (Ephrem).