The influence of the finiteness of the width of the total X-ray reflection region on the angular distribution of diffracted transition radiation of relativistic electrons in crystals is analyzed. Such an effect is investigated for different reflecting planes, diffracted X-ray energies, and electron beam energies and is found to be non-negligible and to substantially change the angular distributions of diffracted transition radiation under certain experimental conditions. The difference between the reflectivity and the δ function is shown to distort the angular distribution of the detected radiation and to limit the possibility of using this type of radiation to diagnose the parameters of beams of relativistic electrons and positrons with energies greater than 50 GeV.