  Inferring line-of-sight distances from redshifts in and around galaxy
clusters is complicated by peculiar velocities, a phenomenon known as the
"Fingers of God" (FoG). This presents a significant challenge for finding
filaments in large observational data sets as these artificial elongations can
be wrongly identified as cosmic web filaments by extraction algorithms.
Upcoming targeted wide-field spectroscopic surveys of galaxy clusters and their
infall regions such as the WEAVE Wide-Field Cluster Survey motivate our
investigation of the impact of FoG on finding filaments connected to clusters.
Using zoom-in resimulations of 324 massive galaxy clusters and their outskirts
from The ThreeHundred project, we test methods typically applied to large-scale
spectroscopic data sets. This paper describes our investigation of whether a
statistical compression of the FoG of cluster centres and galaxy groups can
lead to correct filament extractions in the cluster outskirts. We find that
within 5 R200 (~15 Mpc/h) statistically correcting for FoG elongations of
virialized regions does not achieve reliable filament networks compared to
reference filament networks based on true positions. This is due to the complex
flowing motions of galaxies towards filaments in addition to the cluster
infall, which overwhelm the signal of the filaments relative to the volume we
probe. While information from spectroscopic redshifts is still important to
isolate the cluster regions, and thereby reduce background and foreground
interlopers, we expect future spectroscopic surveys of galaxy cluster outskirts
to rely on 2D positions of galaxies to extract cosmic filaments.
