A Geister shows up in the second time window, which calls into question whether we are seeing Agatha or Lucrezia in that scene.
They first show up on-screen on (v4, p77), riding giant white spiders. They move very quietly on the spiders (v4, p79).
They speak their own distinctive language. We have hints that they may be from another world, or even another dimension.
Farmers tell many stories about them (v4, p79), one of which is (correctly) that they "cause revenants".
The Geisters clearly know all about Agatha, and have been explicitly looking for her. As we see on (v5, p77), they knows that she exists, how old she is, and whose daughter she is. They describe her as having been "stolen" from them -- is that true?
The Geisters are able to command Lucrezia's "lesser servants" (v5, p78).
Note that, while the search for Agatha is critical to their quest, they don't necessarily put up with guff from her (v5, p79).
Their story is told on (v5, p80), which is probably one of the half-dozen most important pages in the story. There is a lot going on here, that tells us much about the crucial history, but it's pretty opaque. There seems a strong implication that Lucrezia and the Other may not be quite as united as they sometimes appear. More of the story is told on (v5, p94-95), although that segment raises more questions than it answers.
They refers to the GG universe as "the shadow world" (v5, p80).