Jesus uses the Shema to point that the inscriptions of God are to be written upon our hearts and our minds, taught to our children, and kept near us. It is God's inscription that is to be important and first in our lives not the inscriptions of a false-man god.

Jesus closes His answer with the famous lines of, "Render therefore to Caesar the things that are Caesar’s; and to God, the things that are God’s." Well, what is Caesar and what is God's?

To the religious Hebrew everything belonged to God. The hearts, minds, children, land, profits, everything was to belong to God. Jesus reminded the questioners of this when He brought up the "image" and "inscription" points. At the other end of the spectrum the Caesar also claimed that everything belonged to him; land, money, goods, worship, and Jerusalem all was claimed by the Caesar. Again, how was Jesus to respond to the trap between the Hebrew law and the Roman law of governance?

Barr tells us this, and I believe he has his finger on something good here:

With one straightforward counter-question, Jesus skillfully points out that the claims of God and Caesar are mutually exclusive. If one’s faith is in God, then God is owed everything; Caesar’s claims are necessarily illegitimate, and he is therefore owed nothing. If, on the other hand, one’s faith is in Caesar, God’s claims are illegitimate, and Caesar is owed, at the very least, the coin which bears his image. Jesus’ counter-question simply invites His listeners to choose allegiances. Remarkably, He has escaped the trap through a clever rhetorical gambit; He has authoritatively refuted His opponents’ hostile question by basing His answer in scripture, and yet, He never overtly answers the question originally posed to Him. No wonder that St. Matthew ends the Tribute Episode this way: "When they heard this they were amazed, and leaving him they went away."

Source: https://drive.google.com/open?id=1I--mLmYADqD5U_Hmv-_ztlasKSAmT2gHI8R1E8S_XUI