Well-intentioned though many people may have imagined that the CIA probably thought they were, their foreign-policy operations were confused, duplicitous failures.
I do understand the basic structure, "Well-intentioned though they were"
But, I can't parse clearly "Well-intentioned though many people may have imagined that the CIA probably thought they were".
It just doesn't seem to be a relative clause though. Could you help me to understand the parenthesis?
My parsing is as follows:
The CIA probably thought (that) many people may have imagined [that they were well-intentioned]
