  We present the analysis of a sample of twenty-four SLACS-like galaxy-galaxy
strong gravitational lens systems with a background source and deflectors from
the Illustris-1 simulation. We study the degeneracy between the complex mass
distribution of the lenses, substructures, the surface brightness distribution
of the sources, and the time delays. Using a novel inference framework based on
Approximate Bayesian Computation, we find that for all the considered lens
systems, an elliptical and cored power-law mass density distribution provides a
good fit to the data. However, the presence of cores in the simulated lenses
affects most reconstructions in the form of a Source Position Transformation.
The latter leads to a systematic underestimation of the source sizes by 50 per
cent on average, and a fractional error in $H_{0}$ of around $25_{-19}^{+37}$
per cent. The analysis of a control sample of twenty-four lens systems, for
which we have perfect knowledge about the shape of the lensing potential, leads
to a fractional error on $H_{0}$ of $12_{-3}^{+6}$ per cent. We find no
degeneracy between complexity in the lensing potential and the inferred amount
of substructures. We recover an average total projected mass fraction in
substructures of $f_{\rm sub}<1.7-2.0\times10^{-3}$ at the 68 per cent
confidence level in agreement with zero and the fact that all substructures had
been removed from the simulation. Our work highlights the need for
higher-resolution simulations to quantify the lensing effect of more realistic
galactic potentials better, and that additional observational constraint may be
required to break existing degeneracies.
