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The Banken (番犬, lit Watchdogs.) or Bloodhounds are a unit sent from "Tōkyō" to assist in security measures regarding the Irie Institution. They consist of trained professionals in military combat from the SDF and are intended to be called only in extreme circumstances. For instance, they are the unit that needs to be called should the need to subdue the Yamainu rise.
Okonogi laments on how he would rather be in charge of the Banken instead of the Yamainu for several reasons; one being the Yamainu

The Banken initially only appear during the ending of Matsuribayashi-hen and Miotsukushi-hen where they are called in by Tomitake Jirō after his escape to Okinomiya. In Matsuribayashi-hen, the Banken surround Takano in order to arrest her, but Tomitake interrupts them. In Miotsukushi-hen they actually try to shoot Takano, but Hanyū takes the bullet and saves Takano. They return in the third season anime-only arc Nekodamashi-hen, similarly summoned by Jirō when Takano decides not to go through with her plans to sacrifice the village.