Before revision:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
After revision:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the strong convergence occurs under more general (not necessarily monotone) sequence of drivers , which is then used to give sufficient conditions for the Malliavin's differentiability.