Mathew Ch 15, verse 21 to 28.
With regard to verse 23 in particular, Jesus's silence.
I do not understand this and would appreciate some thoughts.
I take it the application of this incident to life now is about when we pray but feel Jesus doesn't always appear to hear our cries? Perhaps He is testing our faith.
So when this woman came to Jesus in distress, He seems reluctant to help. Is this because she is of a different faith? So Jesus states that He was sent to take care of HIS own, lost sheep.
Could the fact that He does eventually answer and grant healing to the woman's loved one mean if an atheist or one of a different religion prays, Jesus will heal them?
There is so much to unpack in this passage. Please excuse my brevity and ask clarifying questions if needed.
The woman was from the area of two cities, Tyre and Sidon, in the Canaanite region.
This is our first clue about what is transpiring. In short: those regions, according to the Jews, are under the curse of God. They had it on good account from their prophets:
"Because of the day that comes to plunder all the Philistines,
To cut off from Tyre and Sidon every helper who remains..."
“Therefore thus says the Lord GOD: ‘Behold, I am against you, O Tyre, and will cause many nations to come up against you, as the sea causes its waves to come up."
The burden of the word of the LORD
Against the land of Hadrach,
And Damascus its resting place
(For the eyes of men
And all the tribes of Israel
Are on the LORD);
Also against Hamath, which borders on it,
And against Tyre and Sidon, though they are very wise.
When it comes to receiving the Messiah of the Jews,
the metaphorical deck is stacked against her, if you will.
The disciples certainly believe this.
But Jesus waits on their response. They respond with the racism that is in their hearts (Don't be alarmed by this, even a racist, when he seeks the Lord, may be perfected by Him).
They say to Jesus
“Send her away, for she cries out after us.”
Jesus turns the discussion on its head. What He says next sets up what He is about to do. He says,
“I was not sent except to the lost sheep of the house of Israel.”
It appears that He agrees with the disciples, that He, as the Messiah, is there for the Jews only.
But then He turns to the woman to address her after she cries out
“Lord, help me!”
Now, she just enacted an ancient truth:
"For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him. For “whoever calls on the name of the Lord shall be saved.”
Not all of Israel is Israel. All who call on the name of the Lord shall be saved.
And here, she is about to be saved from her affliction, or rather her daughter's affliction.
But Jesus, wanting to push the issue with His disciples further, replies to the woman according to the colloquialisms of the day, "
aren't you merely a dog?" (this is my paraphrase) effectively giving HER an opportunity to display her faith (Jesus knew this).
She answers
“Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters’ table.”
My paraphrase: "Yes Lord (there is again!) Even the lowest of dogs are fed by the master".
She knew the Deliverer was fer her too!
Jesus answered:
“O woman, great is your faith! Let it be to you as you desire.”
I imagine the heads of the disciples whipped around when they heard Him speak these words. See, this encounter was mainly for the disciples. He knew that those closest to Him must understand that He was sent to "who so ever" and not just the Jews. This passage is another proof that
God so loved the world. 
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