It is significant that we are told this woman is a Greek. 

Jesus was mainly teaching the Jews. That was His mission.

Those that were not Jews were outside of the inner circle - outcasts to a certain degree.

So this woman was not included in that inner circle.

However, she knew about Jesus. 

She sought after Him - even though she knew He may not heal her daughter.

Mark 7:27

We know Jesus is not cruel or mean. 

This verse may seem that way - which is why we need to discuss it in a little more detail.

If you’ve just made dinner - you’ve spent an hour or two on it, and your family sits to eat. Who will have priority? You, your husband, your children, right?

Afterwards, if there are some leftovers maybe you’d let your dog have them. 

Usually the dog doesn’t eat first though (usually of course).

Jesus is reminding her that He is there to teach these people - that is His priority.

Mark 7:28

She is not offended - she understands. 

Really in this response, she’s telling Jesus where her stance is on Him, and His words and teachings.

She is telling Him - I will take the crumbs. I will take what I can have right now while I wait for more to come.

Matthew 15:28

Jesus sees that she’s genuine. She isn’t there just because she has heard of Him. 

She knows Him. She’s heard His teachings. She wants to be a follower of Jesus Christ and knows He can heal her daughter. She pleads with Him to heal. Once He knows her place - she tells her and heals her daughter.

I always love the stories of healings that happen from afar. Those when the people being healed are not in the presence of Jesus Christ.