Re:

My point is that your interpretation of "reasonable" differs from 4th amendment "reasonable" in the context of an administrative search.

The TSO counted the $4710, interrogated the detainee, and then threatened to bring in law enforcement personnel to whom the detainee would be required to answer, and you said "He did not overstep his authority in any way, nor that of the TSA, only the way he interacted with the passenger."

TSA itself investigating the money as a drug crime under the guise of a potential customs violation seems well outside the scope of its warrantless search. If TSA "creates probable cause" by searching more intensely than "no more intrusive or intensive than necessary, in light of current technology, to detect weapons or explosives, " it is no longer "reasonable".