Conversation so far:
Who was the double agent?
Professor X is forced to make Mystique his secret agent, as his previous one, Prudence Leighton, has died and Mystique is the only one suitable to complete the missions.
Who did Mystique turn on to become a double agent?
Quiet Man
Was Mystique forced into turning on quiet man?
No, she created a plan that would free her from both men

Question: Was there a mission or something she went on during this time?
Self-contained rewrite: Was there a mission or something Mystique went on during her time as a double agent?