Fined for what?The inspector asked where the card was. That card is supposed to be displayed outside. The inspector was giving the HO the benefit of the doubt by asking why there was no card outside.
The inspector could have just simply levied a fine and issued a stop order without even talking to the owner.
I don't see this as a search warrant issue, but the HO could have stopped the inspector from coming into the home without one. HO still would have got fined and a stop order issued either way.