What is a Cat's Eye that was referenced in Monogatari Second Season Episode 24 at 08:35?
There's an old manga series called Cat's Eye, which is about a trio of sisters who are art thieves, and hence presumably skillful enough to break into secured places and steal things, or leave things behind, as may be their wont. I assume this is what Kaiki was referencing. 

In the manga, "Cat's Eye" is the name by which the sisters collectively identify themselves (as well as the name of the cafe they operate, among other things).