  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
($M_{corr}(<\theta_E)$ where $\theta_{\rm E}$ is approximated from arc
positions; 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 data 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 need fast, reliable methods to advance the field.
