We place constraints on the dynamics of the Local Group (LG) by comparing the dipole of the cosmic microwave background (CMB) with the peculiar velocity induced by the Two Micron All-Sky Redshift Survey galaxy sample. The analysis is limited by the lack of surveyed galaxies behind the zone of avoidance (ZoA). We therefore allow for a component of the LG velocity due to unknown mass concentrations behind the ZoA, as well as for an unknown transverse velocity of the Milky Way relative to the Andromeda galaxy. We infer extra motion along the direction of the Galactic Centre (where Galactic confusion and dust obscuration peaks) at the 95 per cent significance level. With a future survey of the ZoA it might be possible to constrain the transverse velocity of the Milky Way relative to Andromeda.