How come Eric and Jen never ran into each other in the library, or specifically, at the location of the book; or for that matter, that Ilsa never found them there?
Consider how many notes Eric & Jen leave in the book while in their timeline only about 4-5 months (it's one semester) pass; this comes down to several notes by both of them per day, including weekends; Jen even literally states in her marginalia on pg. 76 that they come get the book to write in it 2 or 3 times each day. They should have ran into each other at the book at one point. Or, considering that Jen works there, she must have seen Eric go to the book and take it at least once.
In that vein: Ilsa suspects Jen and Eric communicate with each other, she knows both are obsessed with Straka's books, and she must know that Jen has a job at the library. So Ilsa must have put two and two together and figured out Jen and Eric communicate with each other at/through the library, and most likely at/through a Straka book. And as a PhD, Ilsa must spend considerable time at the library herself, so she should have seen Jen and/or Eric go to the Straka book.