Are there echoes of gravitational waves?

In several approaches to evading the information paradox, the semiclassical black hole is replaced by an Exotic Compact Object (ECO). It has been conjectured that gravitational waves emitted by the merger of ECOs can reflect off the ECOs and produce a detectable `echo'. We argue that while a part of the wave can indeed reflect off the surface of an ECO, this reflected wave will get trapped by a new closed trapped surface produced by its own backreaction. Thus no detectable signal of the echo will emerge to infinity. The only assumption in this analysis is that causality is maintained to leading order in gently curved spacetime. Thus if echoes are actually detected, then we would face a profound change in our understanding of physics.