We compute the mass and current quadrupole tidal corrections to the
four-momentum and energy flux radiated during the scattering of two spinless
bodies, at leading order in $G$ and at all orders in the velocities, using the
effective field theory worldline approach. In particular, we derive the
conserved stress-energy tensor linearly coupled to gravity generated by the two
bodies, including tidal fields, and the waveform in direct space. The integral
is solved using scattering amplitude techniques. We show that our expressions
are consistent with existing results up to the next-to-next-to-leading order in
the post-Newtonian expansion.
