Abstract: The time-dependent $CP$ asymmetry in exclusive ${B}^{0}(t)\ensuremath{\rightarrow}{K}^{*0}\ensuremath{\gamma}$ decays has been proposed as a probe of new physics in B decays. Recently, this method was extended to radiative decays into multibody hadronic final states such as ${B}^{0}(t)\ensuremath{\rightarrow}{K}_{S}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ and ${B}^{0}(t)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$. The $CP$ asymmetry in these decays vanishes to the extent that the photon is completely polarized. In the standard model, the photon emitted in $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ has high left-handed polarization, but right-handed contamination enters already at leading order in $\ensuremath{\Lambda}/{m}_{b}$ even for vanishing light quark masses. We compute here the magnitude of this effect and the time-dependent $CP$ asymmetry parameter ${S}_{{K}_{S}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}}$. We find that the standard model can easily accommodate values of $S$ as large as $10%$, but a precise value cannot be obtained at present because of strong interactions uncertainties.