We define and study hole-like excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of gray solitons propagating on top of a Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton leads to a finite life-time for the trapped Lieb II mode. It is shown that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.