  The observation of the inspiral and merger of compact binaries by the
LIGO-Virgo collaboration has allowed for new tests of Einstein's theory in the
extreme gravity regime, where gravitational interactions are simultaneously
strong, non-linear, and dynamical. Theories beyond Einstein's can also be
constrained by detecting the polarization modes of gravitational waves. In this
paper, we show that dynamical Chern-Simons and Einstein-dilaton-Gauss-Bonnet
gravity cannot be differentiated from general relativity based on the detection
of polarization modes alone. To prove this result, we use the Newman-Penrose
method and an irreducible decomposition method to find that only the tensorial
modes can be detected in both these theories.
