In the book, Jon intentionally let her go and didn't chase her down. Halfhand, the leader of Jon’s scouting party, left Jon alone with her just to see how he would handle the situation. He didn’t mind if Jon let her go because she was unarmed, alone, and too far from the wildling army to alert them of the scouting party's presence. Since she was not a threat, he found it more useful to see what Jon was capable of rather than killing the girl himself. "To lead men you must know them, Jon Snow. I know more of you than I did this morning."