To understand what's going on in this chapter, read the title: The FOUR Children Consumed by the Mountain. That refers to the four little goblins, the previous victims of kamikakushi. The boy objectively knows that the missing boy DOESN'T NEED TO BE RESCUED. The Lord of the Mountain is kind to the children it kidnaps and they live happily by its side, immortal, eternally young and mischievous. Now, there would be an impact to the people of the outside world, but that's because they don't have this knowledge, and in any case he's a bit of a misanthrope - their emotional pain isn't his problem and will be healed by time anyway.
Therefore, from a strictly objective in-world perspective of the boy, the act of rescuing the missing boy only has value to himself. Subjectively, it would satisfy his desire for personal justification. Objectively, it might have given him a new friend or incognito appreciation from people who care about the missing boy. By the Lord of the Mountain erasing the act, the boy loses all that potential value he could have derived from the rescue. It's an equivalent exchange from both his and the Lord's shared perspective of the unseen world.