Okay, trying to take this slowly.
The Satanists are claiming that they have a consecrated host which they are planning to use. the Archdiocese of Oklahoma City position is that any consecrated hosts are the property of the Church - represented within Oklahoma City by the Archbishop. So far, so simple.
The Church’s claim sets out the value and importance of a consecrated host (which doesn’t have to be valuable) as well as the protection associated with such hosts. The idea behind this is not just to show its importance to the Church but also the care which is taken of such hosts. All of this is intended to show that it could not have been obtained unlawfully - that is, without deception, theft, etc - and should therefore be returned.
The satanists are claiming that they were lawfully given the host (well sent it in the post…) by a Catholic priest (who they notably refuse to name) in another country (which again they refuse to name) which would of course be outside of the court’s jurisdiction. Put simply they’re saying we didn’t steal the host, it was given to us by someone who was allowed to have it and who in fact consecrated us. I get a sense here that they’re saying that it belongs to the priest who consecrated it.
Okay so picking apart the arguments, I see several problems with the Satanists case. First of all, if they’re not going to name (and produce) the priest then they’re on a short road to a hiding (in a legal sense at least) because they’ll have no evidence to support their argument. Of course if they do name and produce their priest, then enquiries can of course be made to determine if he his in fact a real priest. Assuming, they may also run into difficulties from the fact, while in consecrating the host, that he was acting on behalf of the Church but in sending it to the Satanists he was doing something that the Church would not have allowed him to do and the Satanists would (arguably) have known this.
So what this is about it making the Satanists out up or shut up. That is, they can produce their priest (or admit he doesn’t exist) or they can give the host back (or admit it’s not consecrated after all). Overall, it’s not a half bad strategy on the part of the Archdiocese given the seeming raft of Satanic rituals lately. If nothing else it’s likely to deter Satanists from publicity seeking in the future given the cost of hassle of litigation - more so if the Archdiocese is successful.