See this miracle explained in the notes at Matthew 15:21-28.
Would have no man know it - To avoid the designs of the Pharisees he wished to be retired.
A Greek - The Jews called all persons “Greeks” who were not of their nation. Compare Romans 1:14. The whole world was considered as divided into Jews and Greeks. Though she might not have been strictly a “Greek,” yet she came under this general appellation as a foreigner.