An impingement cooling sleeve includes a sleeve body having an inner surface to face a transition duct and an outer surface facing opposite the inner surface. At least one cooling hole is formed within the sleeve body and is used to direct cooling air toward the transition duct. At least one conduit member is attached to the sleeve body and is associated with the at least one cooling hole. The conduit member has a first opening to define an air inlet and a second opening to define an air outlet. In one example, the first opening is spaced apart from the outer surface of the sleeve body by a distance. In one example, the first opening comprises an annular end face surface that defines a plane that is obliquely orientated relative to the outer surface of the sleeve body.