Francesca already mentioned in previous volumes that her to goal is to use the Grail to "clear that Great Labyrinth". The biggest implication here is that she's talking about Caubac's Labyrinth, so the clear condition for it should be taking the Triten (aka Hibiki) out of it. We can't figure out why because we still haven't had the explanation for what the Triten does.
This goal is restated here but worded like this:
I'm so excited. Even the entrance to that pesky
Great Labyrinth is hard to find. But I wonder, when we let the Grail's power clear the maze for us and we get the
miniature of the world hidden on its dephts, how much will we be able to
expose the world?
There's really a lot to unpack here. First, the labyrinth's prize is a miniature of the world, which implies Hibiki is a living Chaldeas. That's really absurd at first glance, but rechecking the information, it actually makes sense. The Triten is described as the conclusion to Caubac's thoughts and Caubac claimed his field of expertise was "defining a destination, then indicating the path to the future by altering the initial conditions". That sounds enough like Rayshifting to solve a Singularity (with the determined destination being the proper hystory) to convice me.
Then there's the part that they want to use that Chaldeas rip-off to "expose the world", which sounds disturbingly familiar to whatever Holmes' shady business is. Suddenly Mahou Tsukai no Hako became the most relevant entry to FGO's current plot.