Based on previous studies on the scattering of Majorana and Dirac fermions in Schwarzschild spacetime and the effects of the torsion on the scattering of the two fermions, under the weak field approximation of gravity and the lowest order approximation of the perturbation of the gravitational field scattering of fermions, this study decomposes the spin connection into a vector-like part under parity transformation and separately analyzes the effects of the two parts on the scattering matrix elements of the two fermions. A difference is found to exist between the general gravitational field on the quantum scattering matrix elements of the two fermions, where the difference derives from the vector-like part. These findings are then verified in the context of the Kerr gravitational field, where the difference between the scattering matrix elements of the two fermions is determined to be related to the mass and angular momentum of the gravitational source. The difference diminishes in the case of Schwarzschild spacetime when the angular momentum is zero.