A turbine engine system includes a gutter and a gear train with an axial centerline. The gutter is disposed radially outside of the axial centerline. The gutter includes an inner surface and a channel that receives fluid directed out of the gear train. The inner surface at least partially defines a bore in which the gear train is arranged. The channel extends radially into the gutter from the inner surface, and circumferentially to a channel outlet. The bore has a cross-sectional bore area, and the channel has a cross-sectional channel area that is substantially equal to or less than about two percent of the bore area.