  For the first detection of a novel astrophysical phenomenon, scientific
standards are particularly high. Especially in a multi-messenger context, there
are also opportunity costs to follow-up observations on any detection claims.
So in searching for the still elusive lensed gravitational waves, care needs to
be taken in controlling false positives. In particular, many methods for
identifying strong lensing rely on some form of parameter similarity or
waveform consistency, which under rapidly growing catalog sizes can expose them
to false positives from coincident but unlensed events if proper care is not
taken. And searches for waveform deformations in all lensing regimes are
subject to degeneracies we need to mitigate between lensing, intrinsic
parameters, insufficiently modelled effects such as orbital eccentricity, or
even deviations from general relativity. Robust lensing studies also require
understanding and mitigating glitches and non-stationarities in the detector
data. This article reviews sources of possible false positives (and their flip
side: false negatives) in gravitational-wave lensing searches and the main
approaches the community is pursuing to mitigate them.
