  Strong gravitational lensing is a powerful tool to measure cosmological
parameters and to study galaxy evolution mechanisms. However, quantitative
strong lensing studies often require mock observations. To capture the full
complexity of galaxies, the lensing galaxy is often drawn from high resolution,
dark matter only or hydro-dynamical simulations. These have their own
limitations, but the way we use them to emulate mock lensed systems may also
introduce significant artefacts. In this work we identify and explore the
specific impact of mass truncation on simulations of strong lenses by applying
different truncation schemes to a fiducial density profile with conformal
isodensity contours. Our main finding is that improper mass truncation can
introduce undesired artificial shear. The amplitude of the spurious shear
depends on the shape and size of the truncation area as well as on the slope
and ellipticity of the lens density profile. Due to this effect, the value of
H0 or the shear amplitude inferred by modelling those systems may be biased by
several percents. However, we show that the effect becomes negligible provided
that the lens projected map extends over at least 50 times the Einstein radius.
