Why did the boys return the horse?

The boys in the story, Aram and his cousin Mourad, always intend to return the horse. At the beginning of the story, about two pages in, we learn that Mourad has been taking the horse for early morning rides "for some time", and, afterward, returning it to its owner before he, the owner, awakes.
The only reason the boys don't return the horse straight away, as usual, is because the horse runs off after throwing Aram from its back. The boys don't catch the horse again in time to return it before the "whole world is awake."
The boys then agree not to return the horse until Aram has learned to ride without being thrown off, but this plan is frustrated by a chance encounter that the boys have with the horse's owner, John Byro. John Byro sees the horse and remarks that it is "the twin" of the horse that was stolen from him. Byro also then says:

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.

John Byro here is not explicitly accusing the boys of stealing his horse, but he is letting them know that the game, as it were, is up. He acknowledges the boys as "sons of my friends," and does not explicitly accuse them of stealing out of respect for, and to preserve the reputation of those friends. He is also deliberately reminding them of the reputation of their family for honesty as a kind of reprimand. In this way he shames them into returning the horse, and, out of respect for their family, who are his friends, he decides not to expose them as thieves.

In this story, Aram and Mourad eventually return the horse to its rightful owner, John Byro, and there are a couple of reasons why they do this.
First of all, the boys never intended to permanently keep the horse. This is made clear early in the story when Aram has had his turn riding the horse. Mourad says that they will either return the horse or hide it until the morning. In fact, it is Aram who convinces Mourad to keep the horse for longer, so that he might learn how to properly ride it.
Secondly, the boys return the horse because John Byro knows that they have taken it. When he comes across them and the stolen horse towards the end of the story, Byro swears that it is his. Although he does not directly accuse the boys of stealing, this encounter with John Byro prompts the boys to return the horse. After all, their tribe is well-known for its honesty. If they did not return the horse at this point, they would sully their tribe's reputation.