Are they anonymous or signed? We have occasionally had such problems. Ours were often anonymously distributed. When we responded we made a point referring to their anonymity and signing our note with contact details an invitation to contact the committee for any further info. The contrast of inviting queries vs. anonymous is helpful.
You might find that she is making herself unpopular all by herself and you might not need to do much.
Your committee could make a point of producing a friendly chatty newsletter which could also include nice polite requests/reminders where necessary about where to put the bins or whatever. Make it clearly ‘official’. By contrast the nasty impolite notes will be seen for what they are.
Your newsletter may not need to directly address the misleading notes but it could provide accurate and more plausible information on some of the topics. In time, the note-writer will lose credibility.