I'm not sure if I see it. If you're not putting a force on the frame, then the frame is not bent, and it doesn't return anything. You have to push in order to recuperate the energy.

If you remove the force so fast that the frame doesn't have the time to return the energy back to you, then it will disperse the energy by ringing. But i don't think it's realistic unless you drive your pedals with hammer strokes.