Extremely accurate shape measurements of galaxy images are needed to probe dark energy properties with weak gravitational lensing surveys. To increase survey area with a fixed observing time and pixel count, images from surveys such as the Wide Field Infrared Survey Telescope (WFIRST) or Euclid will necessarily be undersampled and therefore distorted by aliasing. Oversampled, unaliased images can be obtained by combining multiple, dithered exposures of the same source with a suitable reconstruction algorithm. Any such reconstruction must minimally distort the reconstructed images for weak lensing analyses to be unbiased. In this paper, we use the IMage COMbination (IMCOM) algorithm of Rowe, Hirata, and Rhodes to investigate the effect of image combination on shape measurements (size and ellipticity). We simulate dithered images of sources with varying amounts of ellipticity and undersampling, reconstruct oversampled output images from them using IMCOM, and measure shape distortions in the output. Our simulations show that IMCOM creates no significant distortions when the relative offsets between dithered images are precisely known. Distortions increase with the uncertainty in those offsets but become problematic only with relatively poor astrometric precision. E.g. for images similar to those from the Astrophysics Focused Telescope Asset (AFTA) implementation of WFIRST, combining eight undersampled images (sampling ratio Q=1) with highly pessimistic uncertainty in astrometric registration (\sigma_d~10^{-3} pixels) yields an RMS shear error of O(10^{-4}). Our analysis pipeline is adapted from that of the Precision Projector Laboratory -- a joint project between NASA Jet Propulsion Laboratory and Caltech which characterizes image sensors using laboratory emulations of astronomical data. Comment: 18 pages (screen-readable landscape 2-column), 7 figures, to appear in PASP