$G{\prime }_0$ is the leading-order Landau-Migdal parameter that characterizes the spin-isospin dependent nucleon-nucleon interaction. Consequently, the $G{\prime }_0$ is closely related to the Gamow-Teller resonance (GTR), the beta and double-beta decay rates of finite nuclei, the response of hot and dense nucleonic matter that modifies the neutrino-nucleon absorption rates in core-collapse supernovae (CCSNe) and binary neutron star (BNS) mergers, and finally the critical density for pion condensation in neutron stars. In this letter, for the first time, we report the $G{\prime }_0$ with quantified uncertainty in the framework of Bayesian inference, using a self-consistent standard Skyrme Random Phase Approximation (RPA) model and joint constraints from experimental GTR measurements on ${}^{208}Pb$, ${}^{132}Sn$, ${}^{90}Zr$. Our extracted $G_0\prime$ at saturation density is $0.48\pm 0.034$, which is close to the prediction of a few existing Skyrme models that consider spin-isospin observables but smaller than the traditional ones extracted from pion-exchange models. The reasons for this deviation, like the value of the nucleon effective mass $\frac{m^{*}}{m}$ and the density dependence of $G{\prime }_0$, are investigated. The density-dependent $G_0\prime$ values extracted in this work may guide the construction of new energy density functionals that aims to self-consistently describe the dense matter properties in the spin-isospin channel.