Still I assume in game time this actually took place before Kareth showed up, when the Bluestar answered the question Justice posed about her mom. Only the convo. continued later in actual time.
It still means that IC we all would have been there, and I am just asking what L'Aurel would have asked.
If Justice blurts out the offer and the Bluestar just grabs it... then it happens.

I don't know how things were at the time, nor what he would/did do.
If he doesn't jump at it, then L'Aurel at least would ask Justice: what she thinks memories of Thane will give the rebellion or help the war specifically?
If all Justice can respond with is a need for personal knowledge and it will help the church, it can be delt with later.
By Gertie and Mik being there did Xath or Arhconus say anything? Agree to it, obstain, not say anything?
But personally since we would all be standing around it's an IC thing that should be played out somehow, as we have said with all those pesky IC things that involve the group should.
But at the least can a what happened, order of events for the rest of us 'standing around' be posted IC thread up to the actual final exchange? Just so we know what happened, what was said all that fun