  Strong gravitational lensing offers a powerful probe of the detailed
distribution of matter in lenses, while magnifying and bringing faint
background sources into view. Observed strong lensing by massive galaxy
clusters, which are often in complex dynamical states, has also been used to
map their dark matter substructures on smaller scales. Deep high resolution
imaging has revealed the presence of strong lensing events associated with
these substructures, namely galaxy-scale sub-halos. However, an inventory of
these observed galaxy-galaxy strong lensing (GGSL) events is noted to be
discrepant with state-of-the-art {\Lambda}CDM simulations. Cluster sub-halos
appear to be over-concentrated compared to their simulated counterparts
yielding an order of magnitude higher value of GGSL. In this paper, we explore
the possibility of resolving this observed discrepancy by redistributing the
mass within observed cluster sub-halos in ways that are consistent within the
{\Lambda}CDM paradigm of structure formation. Lensing mass reconstructions from
data provide constraints on the mass enclosed within apertures and are agnostic
to the detailed mass profile within them. Therefore, as the detailed density
profile within cluster sub-halos currently remains unconstrained by data, we
are afforded the freedom to redistribute the enclosed mass. We investigate if
rearranging the mass to a more centrally concentrated density profile helps
alleviate the GGSL discrepancy. We report that refitting cluster sub-halos to
the ubiquitous {\Lambda}CDM-motivated Navarro-Frenk-White profile, and further
modifying them to include significant baryonic components, does not resolve
this tension. A resolution to this persisting GGSL discrepancy may require more
careful exploration of alternative dark matter models.
