Demonstration of the removal of the $K^0_s$ decay from three-pion cumulants. Mixed-charge three-pion correlations are projected against the relative momentum of a mixed-charge pair ($q_{31}^{\pm\mp}$). The $K^0_s$ decay into a $\pi^{+}+\pi^{-}$ pair is visible as expected around 0.4 GeV/$c$. The FSI enhancement of the mixed-charge pair ``31" is also visible at low $q_{31}^{\pm\mp}$. FSI corrections are not applied. Systematic uncertainties are shown by shaded boxes.