  The galaxy-scale gravitational lens B0128+437 generates a quadrupole-image
configuration of a background quasar that shows milli-arcsecond-scale
subcomponents in the multiple images observed with VLBI. As this multiple-image
configuration including the subcomponents has eluded a parametric lens-model
characterisation so far, we determine local lens properties at the positions of
the multiple images with our model-independent approach. Using PixeLens, we
also succeed in setting up a global free-form mass density reconstruction
including all subcomponents as constraints. We compare the model-independent
local lens properties with those obtained by PixeLens and those obtained by the
parametric modelling algorithm Lensmodel. A comparison of all three approaches
and a model-free analysis based on the relative polar angles of the multiple
images corroborate the hypothesis that elliptically symmetric models are too
simplistic to characterise the asymmetric mass density distribution of this
lenticular or late-type galaxy. In addition, the model-independent approach
efficiently determines local lens properties on the scale of the quasar
subcomponents, which are computationally intensive to obtain by free-form
model-based approaches. As only 40% of the small-scale subcomponent local lens
properties overlap within the 1-$\sigma$ confidence bounds, mass density
gradients on milli-arcsecond scales cannot be excluded. Hence, aiming at a
global reconstruction of the deflecting mass density distribution, increasingly
detailed observations require flexible free-form models that allow for density
fluctuations on milli-arcsecond scale to replace parametric ones, especially
for asymmetric lenses or lenses with localised inhomogeneities like B0128.
