There is a phase lag between the discretized system Gt and the continuous-time system G, which grows as the frequency approaches the Nyquist frequency. This phase lag is largely due to the rounding of the fractional time delay. In this example, the fractional time delay is half the sample time.
Discretize G again using a third-order discrete-time all-pass filter (Thiran filter) to approximate the half-period portion of the delay.