We present a new sample of strong gravitational lens systems where both the foreground lenses and background sources are early-type galaxies. Using imaging from Hubble Space Telescope (HST)/Advanced Camera for Studies (ACS) and Keck/NIRC2, we model the surface brightness distributions and show that the sources form a distinct population of massive, compact galaxies at redshifts 0.4 ≲ z ≲ 0.7, lying systematically below the size-mass relation of the global elliptical galaxy population at those redshifts. These may therefore represent relics of high-redshift red nuggets or their partly evolved descendants. We exploit the magnifying effect of lensing to investigate the structural properties, stellar masses and stellar populations of these objects with a view to understanding their evolution. We model these objects parametrically and find that they generally require two Sérsic components to properly describe their light profiles, with one more spheroidal component alongside a more envelope-like component, which is slightly more extended though still compact. This is consistent with the hypothesis of the inside-out growth of these objects via minor mergers. We also find that the sources can be characterized by red-to-blue colour gradients as a function of radius which are stronger at low redshift - indicative of ongoing accretion - but that their environments generally appear consistent with that of the general elliptical galaxy population, contrary to recent suggestions that these objects are pre-dominantly associated with clusters.