I'm Lucy, and I'd be happy to answer your questions today.
You're not obligated to pay your tenant for yard work done on the property that is for his benefit if you told him in advance that you would not pay him, or if he did the work without your knowledge. If he puts a mechanic's lien on the property, you can sue him to have it removed. Alternatively, you could do nothing, wait to see if he tries to take action on the lien, and defend on the basis that you never agreed to have the work done.
A mechanic's lien is for contractors, subcontractors, and material providers who provide at least $15 worth of services "for erecting or repairing a house or other building or appurtenances." N.H. Gen. Stat., Section 447:2. If you're talking about things like mowing and leaf removal, you could argue that he's not entitled to a lien for those reasons. Also note that he's required to provide you with written notice of intent to seek a mechanic's lien before doing any work under Section 447:5. If he didn't do that, he can't win if he places a lien and you wind up in court.
Since he doesn't have a lease, you could also serve him with 30 days notice that you're terminating the lease at any time if you're not comfortable with a tenant who think it's OK to make changes at will to your property and then try to put a lien on it.
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