Game Wardens must follow the same laws as the police do and if a game warden has reason to enter your home they must get a search warrant from a judge before they can enter your home and search without permission.
You can refuse entry to a game warden who requests they come into your home to search for something and tell them they cannot enter your home without a search warrant.
If a game warden comes to your door and asks to come in to search then you should always refuse entry and then if they really have a reason to enter the home they will get a search warrant first.
If they try to force entry into your home without a warrant then you should call the police on them because they have no more power than actual cops do.
Even cops have to have a warrant to enter your home without your permission.