  Scalar-tensor theories leaving significant modifications of gravity at
cosmological scales rely on screening mechanisms to recover General Relativity
(GR) in high-density regions and pass stringent tests with astrophysical
objects. Much focus has been placed on the signatures of such modifications of
gravity on the propagation of gravitational waves (GWs) through cosmological
distances while typically assuming their emission from fully screened regions
with the wave generation strictly abiding by GR. Here, we closely analyse the
impact of screening mechanisms on the inspiral GW waveforms from compact
sources by employing a scaling method that enables a post-Newtonian (PN)
expansion in screened regimes. Particularly, we derive the leading-order
corrections to a fully screened emission to first PN order in the near zone and
we also compute the modifications in the unscreened radiation zone to second PN
order. For a concrete example, we apply our results to a cubic Galileon model.
The resulting GW amplitude from a binary black hole inspiral deviate from its
GR counterpart at most by one part in $10^{2}$ for the modifications in the
radiation zone and at most one part in $10^{11}$ due to next-order corrections
to the fully screened near zone. We expect such modifications to be
undetectable by the current generation of GW detectors, but the deviation is
not so small as to remain undetectable in future experiments.
