We study the inner structure of the group-scale lens CASSOWARY 31 (CSWA 31) by adopting both strong lensing and dynamical modeling. CSWA 31 is a peculiar lens system. The brightest group galaxy (BGG) is an ultra-massive elliptical galaxy at z=0.683 with a weighted mean velocity dispersion of sigma=432+/-31km/s. It is surrounded by group members and several lensed arcs probing up to =~150kpc in projection. Our results significantly improve previous analyses of CSWA 31 thanks to the new HST imaging and MUSE integral-field spectroscopy. From the secure identification of five sets of multiple images and measurements of the spatially-resolved stellar kinematics of the BGG, we conduct a detailed analysis of the multi-scale mass distribution using various modeling approaches, both in the single and multiple lens-plane scenarios. Our best-fit mass models reproduce the positions of multiple images and provide robust reconstructions for two background galaxies at z=1.4869 and z=2.763. Despite small variations related to the different sets of input constraints, the relative contributions from the BGG and group-scale halo are remarkably consistent in our three reference models, demonstrating the self- consistency between strong lensing analyses based on image position and extended image modeling. We find that the ultra-massive BGG dominates the projected total mass profiles within 20kpc, while the group-scale halo dominates at larger radii. The total projected mass enclosed within Reff=27.2kpc is 1.10^+0.02^_-0.04_*10^13^M_{sun}_. We find that CSWA 31 is a peculiar fossil group, strongly dark-matter dominated towards the central region, and with a projected total mass profile similar to higher-mass cluster-scale halos. The total mass-density slope within the effective radius is shallower than isothermal, consistent with previous analyses of early-type galaxies in overdense environments.