A lattice gas model for the A2 + B2 → 2AB reaction system was studied by Monte Carlo simulation in a two-dimensional triangular lattice surface [Phys. Rev. E 69 (2004)046114]. In the model, a reactive window appears and the system exhibits a continuous phase transition to an A+vacancy covered state with infinitely many absorbing states. The critical behaviour was shown to belong to the robust directed percolation (DP) universality class. In this study, we find that as the particle A diffusion is considered, the infinitely many absorbing states for the continuous phase transition change into only two: one is that in which all sites are occupied by particle A and the other is that in which there is only one vacant site and other sites are occupied by particle A. Furthermore,a parity conserving character appears in the system when the particle A diffusion is included. It is found that the critical behaviour of the continuous phase transition changes from the DP class into the pair contact process with diffusion model (PCPD) class and the parity conserving character has no influence on the critical behaviour in the model.