In support of the ICESat-II mission, this paper studies the bias in surface elevation measurements caused by undetected thin clouds. The ICESat-II satellite will only have a 1064 nm single channel lidar on board. Less sensitive to clouds than the 532 nm channel, the 1064 nm channel tends to miss thin clouds. Previous studies have demonstrated that scattering by cloud particles increases the photon path length, thus resulting in biases in ice sheet elevation measurements from space-borne lidars. This effect is referred to as atmospheric path delay. This paper complements previous studies in the following ways: First, atmospheric path delay is estimated over the ice sheets based on cloud statistics from the Geoscience Laser Altimeter System (GLAS) on board ICESat and the Moderate Resolution Imaging Spectroradiometer (MODIS) on board Terra and Aqua. Second, the effect of cloud particle size and shape is studied with the state-of-the-art phase functions developed for MODIS cirrus cloud microphysical model. Third, the contribution of various orders of scattering events to the path delay is studied and an analytical model of the first order scattering contribution is developed. This paper focuses on the path delay as a function of telescope FOV. The results show that reducing telescope FOV can significantly reduce the expected path delay. As an example, the average path delays for FOV=167 µrad (a 100 m diameter circle on the surface) caused by thin undetected clouds by the 1064 nm channel over Greenland and East Antarctica are illustrated.