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.

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