Counterstreaming beams of electrons are ubiquitous in coronal mass ejections (CMEs) - although their existence is not unanimously accepted as a necessary and/or sufficient signature of these events. We continue the investigations of a high-latitude C
ME registered by the emph{Ulysses} spacecraft on January 18,--,19, 2002 (Dumitrache, Popescu, and Oncica, Solar Phys. {bf 272}, 137, 2011), by surveying the solar wind electron distributions associated with this event. The temporal-evolution of the pitch-angle distributions reveal populations of electrons distinguishable through their anisotropy, with clear signatures of i) electron strahls, ii) counter-streaming in the magnetic clouds and their precursors, and iii) unidirectional in the fast wind preceding the CME. The analysis of the counter-streams inside the CME allows us to elucidate the complexity of the magnetic-cloud structures embeded in the CME and to refine the borders of the event. Identifying such strahls in CMEs, which preserve properties of the low $beta < 1$ coronal plasma, gives more support to the hypothesis that these populations are remnants of the hot coronal electrons that escape from the electrostatic potential of the Sun into the heliosphere.