The reflection of a horizontally polarized, impulsive plane wave by a weakly perturbed ionosphere model is considered. A linear electron density profile and a constant collision frequency are assumed for the unperturbed model, and magnetic field effects are neglected. The transient response is formulated as an inverse Fourier transform of the first-order frequency domain solution. For the special case of a thin-layer irregularity, a numerical inverse transform is used to obtain responses that satisfy causality. It is shown that the presence of the thin-layer irregularity is to modify the waveform of the reflected transient.