The problems of controlling invasive species have been emerging as a global issue. In response to these threats, some governmental programs have been proposed for supporting eradication. This article challenges this view by studying the optimal strategies of controlling invasive species in a simple dynamic model. The analysis mainly focuses on deriving policy implications of catchability in a situation where a series of controlling actions incurs operational costs that derive from the fact that catchability depends on the current stock size of invasive species. We analytically demonstrate that the optimal policy sequence can drastically change, depending on the sensitivity of catchability in response to a change in the stock size, as well as on the initial stock. If the sensitivity of catchability is sufficiently high, the constant escapement policy with some interior target level is optimal. In contrast, if the sensitivity of catchability is sufficiently low, there could exist a threshold of the initial stock which differentiates the optimal policy between immediate eradication and giving-up without any control. In the intermediate range, immediate eradication, giving-up without any control, or more complex policies might be optimal. Numerical analysis is employed to present economic intuitions and insights in both analytically tractable and intractable cases.