The mage can conceal any sympathetic connections he has to people, places or things, making it appear that he might know a lover only casually or not know her at all.
Each success allows the mage to decrease the apparent sympathetic connection (p. 114) he has to a single person, place or thing. He might have an Intimate connection to a cabal-mate, but with three successes, he can make that connection appear (to the eyes of anyone who can see it, such as with the Correspondence spell) to be merely an Encountered connection. The true connection is unaffected; it only appears to be more distant.
Guardians of the Veil Rote: Dispersing the Threads
A Guardian who fears that enemies will try to strike at her through friends and loved ones can baffle them by making it appear that connections are more aloof than they truly are.