As a landlord I mailed a lease agreement to the tenant and signed it?
Your lease to the prospective tenant was an offer to rent on those terms. The prospective tenants return of the lease with changes constitutes a counteroffer, and effects a rejection of your offer. Unless you agree to the counteroffer, no binding lease is created. However, if the changes made were insignificant, a court might decide that the prospective tenant had accepted your offer. I would recommend writing back to the prospective tenant that you do not agree to his terms, but you are still willing to rent to him on your terms if he accepts that agreement in writing, without changes, by a date certain.