Before revision:  The result is then used to generalize the existing results on the Malliavin's differentiability of the quadratic BSDEs in the diffusion setup to the quadratic-exponential growth BSDEs with jumps .
After revision:  The result is then used to give sufficient conditions for the Malliavin's differentiability of the quadratic BSDEs in the diffusion setup to the quadratic-exponential growth BSDEs with jumps .