Not sure what a grey market car is. Grey Market usually refers to goods brought to a country in an irregular way and often do not have the same packaging or warranties.
W113 cars were all sold on the open market by authorized dealers.
Some cars were later shipped to another country but these are not referred to as Grey Market cars.
Cars that came to the US after being first sold elsewhere were required to conform to various US safety and emission requirements such as sealed beam headlights, seat belts, speedometers in miles, etc. This was especially enforced in the late 1960's. The process of conforming was called "Federalization".
I've heard that enforcement of these rules was so strict at that time that after replacing Euro headlights with the required sealed beams, the Euro lights had to be destroyed to prevent later reinstallation.
Later on, possibly by the late 70's? the rules were relaxed and the later imported used cars escaped Federalization. They are now riding the US highways with KM speedos, passing flashers that work, and Euro headlights.
Richard M, NYC driving a non-Federalized Italian market 280SL