It's not only extra honey on whatever this deal is, it's also a partial threat.
If not discovered, no harm, the spies that gathered this intel will continue to spy, possibly get better since they aren't good enough or fast enough to report back the appearance of the new wife.
If it is discovered, that plus their stated backup plan of finding a new person to dub "the saint" doesn't just mean finding a new country. It could also mean replacing the leader of THIS country. And with spies about, and violent zealots...escalation by the church could mean assassins and terror attacks, or maybe even just propaganda to oust him as king. What they want is not him, but the power of the position he has in the country he leads. Hell, with the right powers to make these doll, maybe they could literally make a body double of the king. Even a retaliation of outing spies can act as a measure by the church of how stalwart or paranoid he is or becomes.
That's, of course, if they meant to tip that hand. The fact that they didn't know what the unannounced wife looked like, is likely going to be a measure that he uses moving forward. Imagine if she is announced, and then shortly after that a new messenger comes, and she's incorporated her looks...