Their top security clearances, their access to the deepest darkest secrets of intelligence tools, networks, and systems. Would you trust an employee with your biggest secrets if you knew they were retiring soon and very likely to be hired at many times their current salary by some major competitor?
I can imagine there's plenty of "between the lines" stuff you learn as a CIA agent that, while not specifically classified, wouldn't be something you want going to other nations.
Decision making, for example. Someone internal to any organization will gain a sense of the way the organization will respond to certain situations. For something like national security, this can mean a contracted ex-NSA'r could provide another country with a forecast as to how the NSA will react internally to a certain stimuli.
It falls under "Tools, Techniques, and Procedures". It's the same reason anything published or shared is supposed to go through pre-pub even well after you've left one of the three letters.
