  Meneghetti et al. (2020) recently reported an excess of galaxy-galaxy strong
lensing (GGSL) in galaxy clusters compared to expectations from the LCDM
cosmological model. Theoretical estimates of the GGSL probability are based on
the analysis of numerical hydrodynamical simulations in the LCDM cosmology. We
quantify the impact of the numerical resolution and AGN feedback scheme adopted
in cosmological simulations on the predicted GGSL probability and determine if
varying these simulation properties can alleviate the gap with observations. We
repeat the analysis of Meneghetti et al. (2020) on cluster-size halos simulated
with different mass and force resolutions and implementing several independent
AGN feedback schemes. We find that improving the mass resolution by a factor of
ten and twenty-five, while using the same galaxy formation model that includes
AGN feedback, does not affect the GGSL probability. We find similar results
regarding the choice of gravitational softening. On the contrary, adopting an
AGN feedback scheme that is less efficient at suppressing gas cooling and star
formation leads to an increase in the GGSL probability by a factor between
three and six. However, we notice that such simulations form overly massive
subhalos whose contribution to the lensing cross-section would be significant
while their Einstein radii are too large to be consistent with the
observations. The primary contributors to the observed GGSL cross-sections are
subhalos with smaller masses, that are compact enough to become critical for
lensing. The population with these required characteristics appears to be
absent in simulations.
