Unfortunately, I have a different interpretation of that law, and I think there is a question whether it would even apply in this instance.
US CODE: TITLE 18, PART I, CHAPTER 83, § 1725 Postage unpaid on deposited mail matter:
Whoever knowingly and willfully deposits any mailable matter such as statements of accounts, circulars, sale bills, or other like matter, on which no postage has been paid, in any letter box established, approved, or accepted by the Postal Service for the receipt or delivery of mail matter on any mail route with intent to avoid payment of lawful postage thereon, shall for each such offense be fined under this title.
What the law does not say is that "nothing but mail" can be put in a mail box, but instead that nothing mailable can be put in the mailbox unless it has had postage paid.
For reference, here is a US Supreme Court Case which addressed this topic and that law:
There is nothing in that law that says that the neighbor can't tape notes to the outside of the mailbox, and if the note she put on the inside wasn't "mailable matter" and/or of she did not put it in there "with intent to avoid payment of lawful postage" then she may have not violated any federal laws at all. Even if the post office did consider this matter to be a violation of the law, the most that would be likely would be some form of warning (presuming you can prove the note came from the neighbor).
I would still suggest that it would be appropriate to call your local post office and ask how you file a complaint with them regarding the neighbor, and let them take up the matter if they feel it is appropriate. Even a warning from the USPS might have some effect at inhibiting the neighbor from continuing to bother you in this manner. But if you are hoping they are going to fine her, etc., there if very little chance at that.
Unfortunately, I don't think this is going to stop the neighbor. Based on what you have written, the women has some issue and not being able to put notes in your mailbox (if the post office agrees to send her a warning) seems rather unlikely to stop her.
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