The token of Elder Tiankui represents the Elder's personal presence, and the person who possesses the token is tantamount to having the authority of Elder Tiankui.
With this token on him, Fang Lin is effectively the Elder Tiankui himself; if the Inspection Hall were to put Cold Iron Chains on Fang Lin, it would be like trying to chain Elder Tiankui.
Who would dare to do such a thing? Even if Han Qingshuang wanted to target Fang Lin, it would be impossible for her to order her subordinates to chain him up after seeing the token.
Even if she ordered her subordinates to do it, it's likely none would dare actually carry out such an act, which would be nothing short of treasonous.
"Forget it, there's no need for the Cold Iron Chains," Situ Zheng finally spoke up, giving Han Qingshuang a way to step down without losing too much face.