A staged injector in a combustor of a gas turbine. The staged injector may include an injector tube comprising a lateral wall enclosing an injection passageway that extends between an outlet and inlet. An outboard segment of the injector tube may include an exterior face. A cover may be formed about the outboard segment so form a surrounding plenum. The cover may include a side wall that radially overlaps the outboard segment and forms a first portion of the surrounding plenum therebetween. A ceiling wall of the cover may form a second portion of the surrounding plenum. A screening plate may be formed within the side wall of the cover that includes a multitude of apertures configured to fluidly connect the first portion of the surrounding plenum with a feed cavity formed exterior to the side wall.