User blog comment:IamJakuhoRaikoben/Chapter 468: Memory of the Stars, Review./@comment-24546844-20160109233400/@comment-7418318-20160110091224

Plus even though the letters arrived too late at Grammi for her to make it to the Eclipse opening, at least one letter did arrive at Grammi, sincce that's what made her visit Layla in the first place.

So in addition to what ChronoDeus said, Brandish would also have one or more letters in which Layla (probably desperately) asks for the return of the key, so Brandish would "know" that Layla wanted the key even before the meeting took place.