Early on in the preparation of the new Thark hatchlings, Sola, Carter's mother, gives Carter water that gives him the "Voice of Barsoom" (and something with colors).
Later she is marked publicly for shame for giving him the water. Why?
Sola is punished publicly, by adding another brand to her already heavily scarred body, for the crime of allowing John Carter to escape - not for giving him the 'Voice of Barsoom'.
This can be clearly seen in the movie novelisation (by Stuart Moore | Disney editions | 2012)...
"Sola," Tars said, "chain him. Initiate him with the other hatchlings." [..] That night Carter was shaved, swabbed, cleaned, and powdered along with the other newborns. [..] all the hatchlings were put through the same rough process of initiation into Thark society.
He stood chained in the plaza square, watching helplessly as the Tharks performed their barbaric scarification ritual. Tars Tarkas and the others had blamed Sola for Carter's escape. This was her punishment.