Spectroscopic diagnostics of solar coronal plasmas critically depends on the uncertainty in the measured line intensities. One of the main sources of uncertainty is instrumental scattered light, which is potentially most important in low-brightness areas. In the solar corona, such areas include polar and equatorial coronal holes, which are the source regions of the solar wind; instrument-scattered light must thus pose a significant obstacle to studies of the source regions of the solar wind. In this paper, we investigate the importance of instrument-scattered light on observations of equatorial coronal holes made by the Hinode/EIS spectrometer in two different phases of the solar cycle. We find that the instrument-scattered light is significant at all temperatures, and in both regions it amounts to approximately 10% of the average intensity of the neighboring quiet-Sun regions. Such contribution dominates the measured intensity for spectral lines formed at temperatures larger than Log T = 6.15 K, and has deep implications for spectroscopic diagnostics of equatorial coronal hole plasmas and studies of the source regions of a large portion of the solar wind that reaches Earth. Our results suggest that the high-temperature tail in the coronal hole plasma distribution with temperature, however small, is an artifact due to the presence of scattered light.