A three-dimensional time-dependent quantum mechanical approach is used to calculate the reaction probability (P(R)) and the integral reaction cross section (sigma(R)) for both channels of the reaction He + HD+(v = 0, 1, 2, 3; j = 0) --> HeH(D)+ + D(H), over a range of translational energy (E(trans)) on two different ab initio potential energy surfaces (McLaughlin-Thompson-Joseph-Sathyamurthy and Palmieri et al.). The reaction probability plots as a function of translational energy exhibit several oscillations, which are characteristic of the system. The vibrational enhancement of the reaction probability and the integral reaction cross section values are reproduced qualitatively by our calculations, in accordance with the experimental results. The isotopic branching ratio for the reaction decreases in going from v = 0 to v = 1 and then becomes nearly v-independent in going from v = 1 to v =3 on both the surfaces.