We present a formalism for calculating Sommerfeld effects in gravitational waves by combining effective field theory and black hole perturbation theory. While waves originate from localized multipole moments, their observed signatures are modified by long-distance gravitational backgrounds and induced tidal deformations. We derive a general formula for the Sommerfeld factor, including both the magnitude and phase. This formula reveals that for conservative potentials, the phase is precisely half the Compton scattering phase shift. This framework establishes a link between the renormalization of tidal deformations and multipole moments, offering a scalable method to compute high-precision scalar waveforms.