We present 2D hydrodynamical simulations of the tidal interaction between a supermassive black hole binary with moderate mass ratio and the fossil gas disc where it is embedded. Our study extends previous 1D height-integrated disc models, which predicted that the density of the gas disc between the primary and the secondary black holes should rise significantly during the ultimate stages of the binary’s hardening driven by the gravitational radiation torque. This snowplough mechanism, as we call it, would lead to an increase in the bolometric luminosity of the system prior to the binary merger, which could be detected in conjunction with the gravitational wave signal. We argue here that the snowplough mechanism is unlikely to occur. In 2D, when the binary’s hardening time-scale driven by gravitational radiation becomes shorter than the disc’s viscous drift time-scale, fluid elements in the inner disc get funnelled to the outer disc through horseshoe trajectories with respect to the secondary. Mass leakage across the secondary’s gap is thus found to be effective and, as a result, the predicted accretion disc luminosity will remain at roughly the same level prior to merger.