Start a war against the country that helped yours? That would be an incredibly unpopular war, and the only way it would work is if you made the case that Lady Rose was unjustly removed from her position. Which is true, but if she went with them, then they already got the woman who orchestrated their salvation. Plus, Fi is quite happy as a commoner, but kidnapping her would accomplish the same thing as getting her to agree, from their point of view.
EDIT: My point wasn't clear. If it was a war to "save" her instead, it would be an incredibly popular war. If she were imprisoned, and then they got that info, it would be a popular war. I suppose, since becoming a commoner is generally seen as a death sentence for most, it would get some traction, but again, you already won the "prize" so to speak. All that is left is to rub it in the face of the kingdom that ended up losing her.