Living cells adjust their sensing and migratory machinery in response to changes in their environment. In this work, we show that cells of the social amoeba Dictyostelium discoideum modulate the dynamical state of their actin cytoskeleton in response to an external pulse of the chemoattractant cyclic adenosine monophosphate (cAMP). In particular, we focus on a population of cells that exhibits noisy oscillatory cycles of actin polymerization and systematically study receptor-induced transitions in their cytoskeletal dynamics. In response to a short external pulse of cAMP, these cells adopt a noisy quiescent state, before returning to their initial, oscillatory dynamics. The response exhibits a biphasic time profile, with a duration that shows strong variability between cells; it can extend as long as approximately twelve oscillation cycles. We propose a model that is based on a generic nonlinear noisy oscillator. Our theoretical analysis suggests that the transient termination of oscillations in response to a receptor stimulus occurs via a Hopf bifurcation.