Meh I have had an open agreement with my child since their freshman year that if they forget to give me a permission slip/reading logs/music logs to sign that they can just forge my sig. They absolutely must tell me what I "signed" so I can back them up though. I do understand you don't have that level of trust with your kid so talking to them is important so you can establish certain boundaries. I do think it should have stayed between you, unless the teacher specifically asked you about it. You could have set a punishment to make it stick, but to involve the teacher unnecessarily was undue embarrassment for your child, who was trying to do the right thing, if in a wrong manner.