I suggested something during the book tour that Brandon "liked very much".

IMHO, Graendal cast her net the widest she could (she couldn't have Ituralde at her castle for updates every other week, she needed something simple...), and the best compulsion is the one that doesn't go against the person's inner beliefs or instinct.

So, I think when he came to visit her, Graendal compelled Ituralde to obey his King's orders, no matter what they are.

Case in point: Ituralde obeyed Alsalam's plan for the Seanchan despite knowing deep down that it was crazy and almost certainly suicidal. He obeyed each and every one of his crazy orders and counter-orders, even though he knew it made little sense. He questionned the King's sanity, then reasonned out the merchants would not let him rule long if he was out of control. This fits a pattern of compulsion, especially in TGS, when Ituralde reached the "suicidal phase" and was still going on, and his "allies" were still agreing to follow him.

When he got the last letter from Graendal he had gone in hiding, as if he knew deep down that if another letter reached him he would be forced to obey its new orders. It's more than pure loyalty to his friend/king.

All those squabbling nobles from many factions that had suddenly fallen behind Ituralde are also highly suspicious. Whoever they answered to, they probably got similar messages to join Ituralde at that point, or even more simple: they were all compelled to follow Ituralde if one day he asked them for a meeting/alliance. What's also telling, IMO, is the fact those of them who were Dragonsworn were very reluctant to actually follow Rand when he showed up - not very logical. They did follow, because Ituralde agreed to.

I think this is how Graendal macro-managed the country. She didn't compel most people to do very specific missions - that would have forced her to either roam around to update their orders all the time or have each of them come to her regularly. She rather compelled to obey certain sorts of orders. In Ituralde's case, it was specifically the King's, but she had a whole collection of seals at her disposal. Basically, she had courriers do most of the work for her, while she enjoyed her palace. She avoided suspicion that way as well: no one knew where the courriers really came from.