Why did the cousin return the horse to John Byro?

The cousin returned the horse to John Byro because he felt it necessary to do so. His conviction, however, rested on his desire to protect the Garoghlanian family's good name.
Initially, Mourad (Aram's cousin) did not want to return the horse. Both boys enjoyed riding the majestic, beautiful horse. After John Byro visited Aram's home and inquired about his white horse, however, Aram begged Mourad to return the animal. However, Aram made Mourad promise not to return the horse until after he had learned how to ride.
The boys rode the horse for two more weeks. Eventually, they ran into John Byro on their way to stable the horse at a deserted vineyard. The farmer engaged the boys in conversation. During the interaction, John Byro refrained from accusing the boys of theft. Instead, he merely commented that the horse in their possession looked like his stolen horse. John Byro's last comment probably pricked the boys' conscience:

I would swear it is my horse if I didn't know your parents. The fame of your family for honesty is well known to me. Yet the horse is the twin of my horse. A suspicious man would believe his eyes instead of his heart. Good day, my young friends.

Not long after the conversation, Mourad returned the horse to John Byro's stable. Mourad (the cousin) returned the horse to John Byro because of his pricked conscience.