  The core mass of galaxy clusters is both an important anchor of the radial
mass distribution profile and probe of structure formation. With thousands of
strong lensing galaxy clusters being discovered by current and upcoming
surveys, timely, efficient, and accurate core mass estimates are needed. We
assess the results of two efficient methods to estimate the core mass of strong
lensing clusters: the mass enclosed by the Einstein radius
($M_{corr}(<\theta_E)$; Remolina Gonz\'{a}lez et al. 2020), and single-halo
lens model ($M_{\rm{SHM}}(<\rm{e}\theta_{\rm{E}})$; Remolina Gonz\'{a}lez et
al. 2021), against measurements from publicly available detailed lens models
($M_{\rm{DLM}}$) of the same clusters. We use publicly available lens models
from the Sloan Giant Arc Survey, the Reionization Lensing Cluster Survey, the
\Hubble\ Frontier Fields, and the Cluster Lensing and Supernova Survey with
\Hubble. We find a scatter of $18.3\%$ ($8.4\%$) with a bias of $-7.5\%$
($0.4\%$) between $M_{corr}(<\theta_E)$
($M_{\rm{SHM}}(<\rm{e}\theta_{\rm{E}})$) and $M_{\rm{DLM}}$. Last, we compare
the statistical uncertainties measured in this work to those from simulations.
This work demonstrates the successful application of these methods to
observational data. As the effort to efficiently model the mass distribution of
strong lensing galaxy clusters continues, we are in need of fast and reliable
methods to advance the field.
