Third Amendment
No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner . . .
The distinction between police and soldiers might be used to argue that the police were allowed to enter his home against his will, but the police were "quartered" in his home, since the word means "to be stationed or lodged in a specified place".
The Fourth Amendment is also marginal:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures . . .
The police presence was not for the purpose of a search or a seizure. They could argue that there is no protection against unwelcome intrusion if it is not for the purpose of a search or a seizure. I would have permitted the police to enter my home for a reasonable purpose, but they need permission. They have no authority to demand entry without a warrant.
If they go in and occupy the premises without the owner's consent, it IS a seizure.