Thanks to its high spectral resolution (similar to 5 eV at 6 keV), the Soft X-ray Spectrometer (SXS) on board Hitomi enables us to measure the detailed structure of spatially resolved emission lines from highly ionized ions in galaxy clusters for the first time. In this series of papers, using the SXS we have measured the velocities of gas motions, metallicities and the multi-temperature structure of the gas in the core of the Perseus Cluster. Here, we show that when inferring physical properties from line emissivities in systems like Perseus, the resonant scattering effect should be taken into account. In the Hitomi waveband, resonant scattering mostly affects the Fe XXV He alpha line (w)-the strongest line in the spectrum. The flux measured by Hitomi in this line is suppressed by a factor of similar to 1.3 in the inner similar to 30 kpc, compared to predictions for an optically thin plasma; the suppression decreases with the distance from the center. The w line also appears slightly broader than other lines from the same ion. The observed distortions of the w line flux, shape, and distance dependence are all consistent with the expected effect of the resonant scattering in the Perseus core. By measuring the ratio of fluxes in optically thick (w) and thin (Fe XXV forbidden, He beta, Ly alpha) lines, and comparing these ratios with predictions from Monte Carlo radiative transfer simulations, the velocities of gas motions have been obtained. The results are consistent with the direct measurements of gas velocities from line broadening described elsewhere in this series, although the systematic and statistical uncertainties remain significant. Further improvements in the predictions of line emissivities in plasma models, and deeper observations with future X-ray missions offering similar or better capabilities to the Hitomi SXS, will enable resonant scattering measurements to provide powerful constraints on the amplitude and anisotropy of cluster gas motions.