But it can be ridiculously hard to use someone as a banner when they're opposed to you and not currently under your control. Scarlet could start pretending to go insane by starting big commotion in public, which would usually make her unsuitable as any ruler, they could make fake accident and hide her pretending that she's dead for some years, until they secure the border, or make better plans. Maybe even make fake scandal with fake pregnancy with stable-boy, though that could be too much for prideful Scarlet, but would definitely kill her value as Faris princess.
On the other hand, once she was dead, Faris could just claim her execution under falsificated crime as casus belli, without even needing to control her. Hell, they could make fake Scarlet like there were
fake Dimitris or
fake Anastasias, and claim they saved her from execution and can't show her due to fear of Abelbide's assassins. Historically it was much more common to use fake pretenders to the throne you wage war to get, rather than force real one but opposed to you to serve as your cause. Dead Scarlet should be actually more convenient for Faris then live one, since she can't oppose them any longer as her real self.
Frankly, they should even be also able to marry her off to some faraway country, beyond the reach of Faris - I don't remember the precise geography of this world, but if Faris is former empire, with severe money problems, they shouldn't be able to invade bigger countries on other continents just for to get their missing royal scion, especially landlocked ones that would need you to conquer or go through with your army through coastal country on another continent first. And another big country could want to keep Faris away from symbol of their former glory, while giving themselves option to keep the famous bloodline in their aristocracy.