I'm guessing that you used a "coming soon" sign in the yard....if so, the interest is to be expected, but is your contact number, QR code or website info listed for inquiries?
Firstly, talk to your broker. I wouldn't ask them to do anything about it quite yet.
Secondly, I would call the agent and ask them to direct any correspondence through you. I would also coach your seller on how to handle situations where other agents may be contacting them.
If the agent does not agree to direct questions through you, I would then ask your broker to contact their broker so that everyone knows what is going on.
Unfortunately, unless there is a signed agreement and people are aware of it, the home owners would be fair game. It's one thing to expect people to be ethical but another to expect them to clairvoyant.
But, so what?
You have a signed and dated contract to LIST the house, and the Sale of the house is not CONTINGENT upon it appearing on the MLS.
This is actually a question that should have gone to your Broker; that's what he's there for.