Yes, a note would work.
Essentially I am looking at this from the perspective of the father of a teenage girl, as well as that of a "legal expert". As a father, if a teenage boy wanted my daughter to "stay over" I would emphatically say "no!", because what comes to mind is sex. And I would to do all I could to protect my child from bad decisions in that respect.
I don't know what your attitude is in that regard. But a responsible parent of the 17 year old girl, in this situation, would have to be well assured that you would be a responsible chaperone.
Lawyer.
27 years practice of law