Gauss-Bonnet Dark Energy has been a popular model to explain the accelerated expansion of the Universe. Quite generically it also predicts the speed of gravitational waves c_GW to be different from the speed of light. This fact alone led some authors to exclude such models in view of the new tight observational constraints on c_GW. However, the behaviour of c_GW depends on the choice of the Gauss-Bonnet (GB) coupling function. It is possible to construct models where c_GW is always equal to the speed of light. More generally, c_GW is a time dependent function with instances where both speeds coincide. Nevertheless, we observe that the bound on c_GW excludes scenarios where the GB term directly affects the expansion of the Universe, even if the constraint on the variation of the coupling function does not appear to be strong. We perform the dynamical systems analysis to see if the expansion of the Universe could be affected indirectly by modulating the behaviour of the scalar field, which modulates the GB coupling. It is shown that either the bounds on c_GW are violated by many orders of magnitude, or it might be very difficult to find models that are consistent with other cosmological observations.