The paper revisits the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the one-loop level (order $G^3$) and compares it with the corresponding multipolar-post-Minkowskian (MPM) waveform. The authors reorganize the one-loop five-point amplitude to remove spurious poles, simplifying the post-Newtonian expansion. They find complete agreement between the two approaches up to the fifth order in the small velocity expansion, after accounting for three subtle aspects: (1) a frame rotation by half the classical scattering angle, (2) an additional finite term from dimensional regularization, and (3) contributions from zero-frequency gravitons at orders $G^1$ and $G^3$. The paper also discusses the role of zero-frequency gravitons in resolving differences between the amplitude-based and MPM results, and their implications for Bondi-Metzner-Sachs supertranslations.The paper revisits the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the one-loop level (order $G^3$) and compares it with the corresponding multipolar-post-Minkowskian (MPM) waveform. The authors reorganize the one-loop five-point amplitude to remove spurious poles, simplifying the post-Newtonian expansion. They find complete agreement between the two approaches up to the fifth order in the small velocity expansion, after accounting for three subtle aspects: (1) a frame rotation by half the classical scattering angle, (2) an additional finite term from dimensional regularization, and (3) contributions from zero-frequency gravitons at orders $G^1$ and $G^3$. The paper also discusses the role of zero-frequency gravitons in resolving differences between the amplitude-based and MPM results, and their implications for Bondi-Metzner-Sachs supertranslations.