We calculate the tidal corrections to the loss of angular momentum in a two-body collision at leading post-Minkowskian order from an amplitude-based approach. The eikonal operator allows us to efficiently combine elastic and inelastic amplitudes, and captures both the contributions due to genuine gravitational-wave emissions and those due to the static gravitational field. We calculate the former by harnessing powerful collider-physics techniques such as reverse unitarity, thereby reducing them to cut two-loop integrals, and cross check the result by performing an independent calculation in the post-Newtonian limit. For the latter, we can employ the results of P. Di Vecchia et al. [Angular momentum of zero-frequency gravitons, J. High Energy Phys. 08 (2022) 172.JHEPFG1029-847910.1007/JHEP08(2022)172], where static-field effects were calculated for generic gravitational scattering events using the leading soft graviton theorem.