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 +/- 31 km s(-1). It is surrounded by group members and several lensed arcs probing up to (sic)150 kpc in projection. Our results significantly improve on 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, in both 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 20 kpc, while the group-scale halo dominates at larger radii. The total projected mass enclosed within R-eff = 27.2 kpc is 1.10-(+0.02)(0.04) x 10(13) M-?. We find that CSWA 31 is a peculiar fossil group, strongly dark-matter dominated toward 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.