As an urban legend, I've heard this claim many times. Allegedly, in the 1970s, the KGB sponsored various Western "anti-war" movements, especially the ones that could hinder Western nuclear tests. As a matter of fact, Greenpeace was one such movement, created in response to nuclear testing in Alaska, which allegedly earned them the help of the KGB. Quite vague claims. However, recently, I've seen political discussion where more concrete claims were made. Allegedly, the original Rainbow Warrior, after being bought by Greenpeace, was refurbished in a shipyard in Tallinn at the KGB's expense. Allegedly, the information comes from the Mitrokhin Archive.
Is there any truth to any of these claims?