We are conducting a search for new gamma-ray binaries by making high signal-to-noise light curves of all cataloged Fermi LAT sources and searching for periodic variability using appropriately weighted power spectra. The light curves are created using a variant of aperture photometry where photons are weighted by the probability that they came from the source of interest. From this analysis we find that the light curves of a number of sources near the ecliptic plane are contaminated by gamma-ray emission from the Moon. This shows itself as modulation on the Moon's sidereal period in the power spectra. We demonstrate that this contamination can be removed by excluding times when the Moon was too close to a source. We advocate that this data screening should generally be used when analyzing LAT data from a source located close to the path of the Moon.