Conversation so far:
Who was the double agent?
Mystique.
Who did she turn on to become a double agent?
United States Civil Service.
Was she forced into this decision?
Professor X is forced to make Mystique his secret agent.

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 being Professor X's secret agent?