The general relativistic (GR) impact is assessed on the precision of the announced BepiColombo (BC) space positions at the Earth, Venus and Mercury flyby points providing planned gravity-assists. Apart of the known elliptic orbit precession, another recently specified for the Schwarzschild-Kerr metric effect of the ellipse axes contraction is considered in the thoroughly built model of BC motion from the launch point to the first assigned flyby point at Venus. The intermediate Earth gravity-assist act is shown to serve as an amplifier of the GR effects, so that the total GR-caused position shift at Venus can reach great distances, exceeding the accuracy of the assigned lengths thousands of times. Similar factors entailing possible GR deviation from BC-Mercury expected flyby points are also analysed. © 2019 The Author(s)