The parameter “Min Move Distance” shown in the screenshot is not exposed via scripting and is also missing from scripting documentation (Unity - Scripting API: CharacterController).
The manual page for Character Controller does indeed show the parameter Unity - Manual: Character Controller component reference
I’m actually unable to even get at this value with reflection. This makes it impossible to assemble a Character Controller based object completely with code.
There is currently an open ticket on this from 2013… https://feedback.unity3d.com/suggestions/charactercontroller-min-move-dis