Dividend policies play a pivotal role in financial management by aiming to maximize shareholders' interest and effectively managing risk. In this paper, we explore the optimal dividend strategy in a discrete-time compound binomial dual risk framework. This model is suitable for a company whose income comes from occasional operating expenses and settlements only once per unit of time. We assume that expenses are subject to dynamic changes influenced by economic factors, following a Markov chain. With or without a ceiling constraint on dividend payments, we prove that the optimal value function serves as the exclusive solution to a discrete Hamilton-Jacobi-Bellman (HJB) equation through the utilization of the fixed-point theorem. Furthermore, we derive a straightforward computational approach for determining the optimal strategy. Finally, we provide numerical examples to illustrate the theoretical findings and calculation methods.