In recent years, the control of the larch budmoth has attracted a great deal of attention from experts, and spraying with insecticides is one of the main control strategies. The key of this strategy is the timing and efficiency of insecticide applications and how multiple insecticide applications affect the growth of budmoth. This paper extends a new two dimensional discrete model by adding chemical controls based on a dynamical model of plant quality interacting with larch budmoth proposed in the literature to cope with this problem. First, the parametric conditions required for the existence and local stability of the positive fixed point of the model are discussed, and under certain conditions, the presence of period-doubling bifurcation and Neimark-Sacker bifurcation of the system, which reveals a significant effect of the kill rates of insecticides on the budmoth growth. The results show that a paradox arises when low kill rates stimulate the growth of budmoth and high kill rates inhibit the growth of budmoth. Furthermore, we analyze the influence of various factors and cumulative effects on the paradox phenomenon. Therefore, the timing of insecticide application and its efficiency should be chosen wisely to prevent the paradox.