Where Cluster Galaxies Reside and How Strongly They Lens

The efficiency of galaxy-galaxy strong lensing (GGSL) in clusters depends jointly on the inner mass distributions of member galaxies and their locations within the cluster potential. Observed GGSL probabilities exceed Λ CDM predictions by nearly an order of magnitude, but the relative roles of internal structure and environment remain unclear. We disentangle these effects by comparing HST strong-lensing clusters with TNG-Cluster analogs at similar lens redshifts, matched by their primary Einstein radius. For each member, we measure its lensing strength in isolation and when embedded in the cluster field. Members in cluster-critical regions are classified as Major or Minor Perturbers depending on whether they strongly lens in isolation; those in subcritical regions are classified as Intrinsic Lenses, Boosted Lenses, or Inert Members according to whether they lens independently, only with environmental assistance, or not at all. Observed clusters contain 33.7% of selected members in cluster-critical regions, compared with 21.6% in TNG-Cluster, while their Major-to-Minor ratios are similar. Outside these regions, observations contain substantially more Intrinsic and Boosted Lenses and fewer Inert Members, with Boosted Lens fractions of 25.8% and 13.5%, respectively. The discrepancy persists at fixed subhalo mass and after including line-of-sight structure. A mass-conserving contraction mimicking core-collapsed self-interacting dark matter largely recovers the conditional lensing fractions but not cluster-critical occupancy. The GGSL discrepancy therefore reflects both insufficient central concentration in simulated members and differences in their locations within the cluster lensing field.