Integrity Committee Transparency Act of 2019 This bill expands the membership of the Council of Inspectors General on Integrity and Efficiency to include a former inspector general and revises requirements regarding the council's Integrity Committee. The Integrity Committee must provide additional information to (1) the council when requesting an extension of time to evaluate an allegation of wrongdoing, and (2) Congress and the council when it closes an allegation without referral to the council for investigation. The committee must brief congressional committees on its activities every six months.