This paper deals with a simple model of bidirectional dimer-monomer reaction over a modified catalyst surface, studied by means of the Monte Carlo simulation method. It is assumed that certain active sites of a catalyst surface are blocked by modifier (or poison) atoms and thus unable to catalyze the reactions. The influence of the modifier species concentration and the topography of their distribution on the reaction yield and selectivity is also discussed. Four types of the modifier spatial distributions are used: random, dendritic, compact and also highly ordered patterns corresponding to the stripes of inactive sites. The assumed model predicts that the reaction occurring between the same partners leads to different products depending on the state of the reacting molecules, which is directly related to the state of the adsorbing sites in the vicinity of the reacting particles. It is demonstrated that the surface concentration of the different types of sites and the topography of their distribution over the surface are both important factors, which influence the behavior of systems considered here. In particular, it has been found that the reaction direction, the reaction window location and its width depend strongly on the surface morphology. The most surprising finding is that some topographies of the modifier species related to the stripes of inactive sites can generate an unusual double reaction window.