Rachel is not, in fact, a Hyde fangirl, though I could see how you might mistake her for one. (Her dialogue here is intended to mimic what used to be referred to as "cinnamon roll" posts on Tumblr.)
This week on Gruesome Victorian Facts You Didn't Ask For, a.k.a. The Butchering Art:
Victorian operating theaters were notoriously unsanitary. Since germ theory hadn't been discovered yet, there was no real motivation for cleaning the theater between operations.
Upon entering the theater, the surgeon would exchange his outside-wear coat with his surgical coat, which was often caked with dried blood and other viscera. Dried blood could also be found seeped into the wooden--wooden--operating table as well as the floor and probably anywhere else blood could gush out onto. At the Old Operating Theatre in London, blood would sometimes drip through the floor of the operating theater through the roof of the church below it (which sounds like an awfully Catholic thing to happen, although I'm pretty sure the church was Anglican).
All this to say that while Lanyon is definitely suspicious about the blood on Jekyll's shirt, it wasn't super uncommon for Victorian doctors to run around covered in other people's blood.