The blue-eyed man was a mysterious employee of the Three Families.
He approached PR woman Jilly Kitzinger to tell her that his employers took an interest in her, particularly in her expert handling of convicted killer and paedophile Oswald Danes whom Kitzinger had turned into a celebrity. (TV: The Categories of Life)
Later, he approached Kitzinger to tell her that her intern, Shawnie Yamaguchi, was an undercover CIA agent. He shot Yamaguchi and offered Kitzinger a job with the Families. (TV: End of the Road)
Later, he supplied Kitzinger with an alias and a ticket to Shanghai to assist the Families there. He told her she wouldn't be seeing him again. (TV: The Gathering)
Nevertheless, some time later, the man met with Kitzinger again. He invited her to assist the families with their new plan, plan B. (TV: The Blood Line)