I'm letting you guys know I'm changing to the harsher plan so we don't kill the demon immediately. Some of you are voting for my name.
I'll say that I think the demons restrictions on travel are way too harsh. She'd be traveling by ship at best if she decides on Essos, and would have no clues other then the agents last know location. Which we learned several years ago. I think it should be 5 years instead of 3, and maybe the periodically returning to Westeros should be changed too because that's a lot of travel.
She could search for years an not find the guy until he started ramping up for the Others return, if she does at all. That's why I said it was a long shot and wanted to make a trading expedition out of it, both as a cover, as a legitimate investment, and as an excuse to give her resources which she could use to track him down.
P.S. Oh wow... you were all voting for my name. Sorry, but it change my vote or never or kill her immediately. I want to see more of this character. If she's legit, maybe she can contact the Children.