  We demonstrate and measure the impact of source galaxy clustering on
higher-order summary statistics of weak gravitational lensing data. By
comparing simulated data with galaxies that either trace or do not trace the
underlying density field, we show this effect can exceed measurement
uncertainties for common higher-order statistics for certain analysis choices.
Source clustering effects are larger at small scales and for statistics applied
to combinations of low and high redshift samples, and diminish at high
redshift. We evaluate the impact on different weak lensing observables, finding
that third moments and wavelet phase harmonics are more affected than peak
count statistics. Using Dark Energy Survey Year 3 data we construct null tests
for the source-clustering-free case, finding a $p$-value of $p=4\times10^{-3}$
(2.6 $\sigma$) using third-order map moments and $p=3\times10^{-11}$ (6.5
$\sigma$) using wavelet phase harmonics. The impact of source clustering on
cosmological inference can be either be included in the model or minimized
through \textit{ad-hoc} procedures (e.g. scale cuts). We verify that the
procedures adopted in existing DES Y3 cosmological analyses (using map moments
and peaks) were sufficient to render this effect negligible. Failing to account
for source clustering can significantly impact cosmological inference from
higher-order gravitational lensing statistics, e.g. higher-order N-point
functions, wavelet-moment observables (including phase harmonics and scattering
transforms), and deep learning or field level summary statistics of weak
lensing maps. We provide recipes both to minimise the impact of source
clustering and to incorporate source clustering effects into forward-modelled
mock data.
