I don’t think Tom “gave it away” he didn’t even know it existed. Jenn thought it was her diary, until she discovered it was locked and realized it was Lenamare’s etc.
It would make sense for Jenn to return it, since she worked for Lenamare (so to speak) and she knew he needed/it wanted it. All part of the team thing.
Also it’s not clear that at first, the students knew why Exador was invading, they thought it was a land grab or other political move.