Kali and Ren are fixated on the rat's master or Ramile's employer because of different reasons.
For Ren the Rat's master intention as to why ignite a rebellion, was he from the empire? What is their ultimate goal? And Ren desires to stop him from destroying the Millano Kingdom.
As Kali, it was simply to know how much this person knows about the case from five years ago and it coincidentally lines up with her promise to Ren to help him stop the empire's meddling or worst subjugation.
Even though they are in possession of the rat, it's master remains unknown because of the Contractual Pledge.
Unlike the pledge letter which binds the action to the paper, when the pledge is fulfilled it turns to ashes and when not the paper turns black and the ink turns white, Contractual Pledge is different, the contract binds the person itself, though not the human's will but it can be part of the body or his life itself.