  Understanding the distribution and occurrence rate of small planets was a
fundamental goal of the Kepler transiting exoplanet mission, and could be
improved with K2 and TESS. Deriving accurate exoplanetary radii requires
accurate measurements of the host star radii and the planetary transit depths,
including accounting for any "third light" in the system due to nearby bound
companions or background stars. High-resolution imaging of Kepler and K2 planet
candidate hosts to detect very close (within ~0.5") background or bound stellar
companions has been crucial for both confirming the planetary nature of
candidates, and the determination of accurate planetary radii and mean
densities. Here we present an investigation of the effect of close companions,
both detected and undetected, on the observed (raw count) exoplanet radius
distribution. We demonstrate that the recently detected "gap" in the observed
radius distribution (also seen in the completeness-corrected distribution) is
fairly robust to undetected stellar companions, given that all of the systems
in the sample have undergone some kind of vetting with high-resolution imaging.
However, while the gap in the observed sample is not erased or shifted, it is
partially filled in after accounting for possible undetected stellar
companions. These findings have implications for the most likely core
composition, and thus formation location, of super-Earth and sub-Neptune
planets. Furthermore, we show that without high-resolution imaging of planet
candidate host stars, the shape of the observed exoplanet radius distribution
will be incorrectly inferred, for both Kepler- and TESS-detected systems.
