{\rm BMO}(\mathbb{R}^n)$, let $\widetilde{\mathcal{M}}_{\Omega,\,b}$ be the commutator of $\widetilde{\mathcal{M}}_{\Omega}$ defined by $$\widetilde{\mathcal{M}}_{\Omega,\,b}f(x)=\Big(\int^0_0\sum_{j\in\mathbb{Z}}\big|F_{j,\,b}