Terahertz(THz)-driven dielectric-lined waveguides have applications in electron manipulation, particularly acceleration, as the use of dielectric allows for phase velocities below the speed of light. However matching a single frequency to the correct velocity does not maximise electron-THz interaction; waveguide dispersion typically results in an unmatched group velocity and so the pulse envelope of a short THz pulse changes along the length of the structure. This reduces field amplitude and therefore accelerating gradient as the envelope propagates at a different velocity to the electron. The effect on net acceleration is demonstrated via an example of a structure excited by a THz pulse of different temporal lengths.