  We study the radial and azimuthal mass distribution of the lensing galaxy in
WFI2033-4723. Mindful of the fact that modeling results depend on modeling
assumptions, we examine two very different recent models: simply parametrized
(SP) models from the H0LiCOW collaboration, and pixelated free-form (FF) GLASS
models. In addition, we fit our own models which are a compromise between the
astrophysical grounding of SP, and the flexibility of FF approaches. Our models
consist of two offset parametric mass components, and generate many solutions,
all fitting the quasar point image data. Among other results, we show that to
reproduce point image properties the lensing mass must be lopsided, but the
origin of this asymmetry can reside in the main lens plane or along the line of
sight. We also show that there is a degeneracy between the slope of the density
profile and the magnitude of external shear, and that the models from various
modeling approaches are connected not by the mass sheet degeneracy, but by a
more generalized transformation. Finally, we discuss interpretation degeneracy
which afflicts all mass modeling: inability to correctly assign mass to the
main lensing galaxy vs. nearby galaxies or line of sight structures. While this
may not be a problem for the determination of $H_0$, interpretation degeneracy
may become a major issue for the detailed study of galaxy structure.

Astrophysics of Galaxies