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 at least partially circumscribes the gear train, and includes an inner surface and a channel. The channel receives fluid directed out of the gear train. The channel extends radially into the gutter from the inner surface to a channel end, and circumferentially to a channel outlet. At least a portion of the channel has a cross-sectional channel geometry that tapers axially as the channel extends radially towards the channel end.