When a Newtonian bubble ruptures, the film retraction dynamics is controlled by the interplay of surface, inertial, and viscous forces. In case a viscoelastic liquid is considered, the scenario is enriched by the appearance of a new significant contribution, namely, the elastic force. In this paper, we investigate experimentally the retraction of viscoelastic bubbles inflated at different blowing rates, showing that the amount of elastic energy stored by the liquid film enclosing the bubble depends on the inflation history and in turn affects the velocity of film retraction when the bubble is punctured. Several viscoelastic liquids are considered. We also perform direct numerical simulations to support the experimental findings. Finally, we develop a simple heuristic model able to interpret the physical mechanism underlying the process.