This is either deep lore or a contradiction, but. My understanding is that the Hedgehog Court are using the Vekeshi to do their dirty work (attack fey targets) in exchange for fey backing and power, like using the Dreaming for their initiations. 'The mirror comes from the Unseen Court' is a lie.
It's all in Book 9: The Hedgehog Court has denounced Risur’s industrial revolution, and has stoked tensions and anger among the ‘common’ fey. It has also offered aid to adherents of the traditional druidic faith in the real world, fought proxy battles through contacts in the Vekeshi Mystics, and given favors to saboteurs like the ‘fey terrorist’ Hana Soliogn, known as Gale.
Olazdor, Archfey of the Winds and Hedgehog lord: ...He quietly aided Ekosissigan’s plan to assault Cauldron Hill in Adventure Five, Cauldron-Born, and had hoped to recruit Gale to be both his ally and his queen.
Now, why would the mirror impact Gale? Well, something Book 2 doesn't do a great job setting up is that Gale really likes the fey, and that matters for Book 5: She met with Ekossigan, and he played to her desires of being accepted by the fey, sweeping her up in a narrative of making a grand difference to the world.
This is part of a big issue with the Vekeshi Mystic theme. It is both the 'fey theme' and the 'Elfaivaran Theme', and it doesn't communicate that.