  We use nine different galaxy formation scenarios in ten cosmological
simulation boxes from the EAGLE suite of {\Lambda}CDM hydrodynamical
simulations to assess the impact of feedback mechanisms in galaxy formation and
compare these to observed strong gravitational lenses. To compare observations
with simulations, we create strong lenses with $M_\star$ > $10^{11}$ $M_\odot$
with the appropriate resolution and noise level, and model them with an
elliptical power-law mass model to constrain their total mass density slope. We
also obtain the mass-size relation of the simulated lens-galaxy sample. We find
significant variation in the total mass density slope at the Einstein radius
and in the projected stellar mass-size relation, mainly due to different
implementations of stellar and AGN feedback. We find that for lens selected
galaxies, models with either too weak or too strong stellar and/or AGN feedback
fail to explain the distribution of observed mass-density slopes, with the
counter-intuitive trend that increasing the feedback steepens the mass density
slope around the Einstein radius ($\approx$ 3-10 kpc). Models in which stellar
feedback becomes inefficient at high gas densities, or weaker AGN feedback with
a higher duty cycle, produce strong lenses with total mass density slopes close
to isothermal (i.e. -d log({\rho})/d log(r) $\approx$ 2.0) and slope
distributions statistically agreeing with observed strong lens galaxies in
SLACS and BELLS. Agreement is only slightly worse with the more heterogeneous
SL2S lens galaxy sample. Observations of strong-lens selected galaxies thus
appear to favor models with relatively weak feedback in massive galaxies.
