Befriending the Rats on Zheng Shi is referred to as 'goodCEO' in code. In game it's measured by an attitude scale in the codex after they discern you are the CEO. After four wins or losses cumulatively, the fifth encounter has the rats learn that you are Victor Steele's son/daughter. This unlocks the reputation scale and when you [Be Nice] to them or [Offer Oral]/[Offer Milk] it goes up. When you max it out you can tell them to stop treating you like a corpo fiend.
Raising the reputation to 50+ is necessary for activating the Christmas event. Befriending the rats is necessary to unlock the cousin/Feruze event.