Thomas Putnam's grievance over land is between him and John Proctor. It involves who has the right to take timber off of a certain piece of land. Both men claim that the land is theirs.
The argument between the two men over this issue is found in Act I, Scene 2. Proctor says that he bought the land five months ago from Mr. Nurse. Putnam claims that the land was in his grandfather's will. Proctor then asserts that Putnam's grandfather was in the habit of claiming land that was not his own.