Let's think about what the sentence is saying and then what it is doing.
It is equivalent (in truth value) to the following propositions:
- The statement "Jill wrote the note" is not necessarily true.
- The statement "Jill wrote the note" may/might not be true.
Proposition 1 is true if and only if something like 1a is true:-
1a. The statement "Jill did not write the note" does not contradict anything we know to be true about Jill or the note.
Proposition 2 looks (and is) more uncertain than this. "May"/"might" are modal forms. If I say "I might/may come and see you tomorrow", my appearance or non-appearance at your house tomorrow makes no difference to the truth or otherwise of my statement. It is not a prediction or a promise. It is modal. So is 'need' as in 'She need not have' done it. If it turns out that she did in fact do the deed, even this does not make the sentence wrong.
As to 'deontic', meaning 'to do with obligation or necessity'. The Routledge Encyclopaedia of Philosophy explains it thus:
Modality, as it is usually understood in contemporary philosophy, has to do with necessities and possibilities. Deontic modality is a kind of modality which has to do with what is necessary or possible according to various rules, such as the norms of morality, the principles of practical rationality or the laws of some country. Deontic modality can be contrasted with alethic modality and epistemic modality. The former has to do with what propositions are necessarily or possibly true given various metaphysical, logical or nomological laws. The latter has to do with what propositions are necessarily or possibly true given various bodies of evidence or information.
Words commonly thought to express deontic modalities include the auxiliary verbs ‘must’, ‘have to’, ‘may’, ‘can’, ‘should’ and ‘ought to ’... On these criteria, I think it would be fair to use the term deontic.