Bragg grating reflectors etched in amorphous silicon overlay films have been integrated with Ti:LiNbO₃ optical waveguides to obtain a narrow \left(0.05\text{\hspace{0.17em} nm}\right) reflectance spectrum with a >20\text{\hspace{0.17em} dB} dip in the transmittance spectrum. These results were realized at a wavelength of \text{1542 .7 \hspace{0.17em} nm} for TE polarization on an x-cut, y-propagating substrate with gratings etched to a depth of \sim \text{93 \hspace{0.17em} nm} in a \text{105 \hspace{0.17em} nm} thick silicon film over a length of \text{12 .5 \hspace{0.17em} mm} . The reflectance in the channel waveguides is found to be strongly dependent on the depth of the etched grating. The effect of the Bragg waveguide loss factor on the transmittance and reflectance spectra is investigated by using a model for contradirectional coupling that includes an attenuation coefficient. The values for coupling constants κ and amplitude attenuation constants α of samples etched for different time durations to control the grating depths are obtained from the model through the use of the depth of the dips in the transmittance spectra and the spectral widths of the reflectance peaks. It is concluded that the corrugated Si overlay film increases the insertion loss by \sim \text{2 .7 \hspace{0.17em} dB} , and the loss is not significantly affected by the grating depth.