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