  The time delay measured between the images of gravitationally lensed quasars
probes a combination of the angular diameter distance to the source-lens system
and the mass density profile of the lens. Observational campaigns to measure
such systems have reported a determination of the Hubble parameter H0 that
shows significant tension with independent determination based on the cosmic
microwave background (CMB) and large scale structure (LSS). We show that lens
mass models that exhibit a cored component, coexisting with a cusp, probe a
degenerate direction in the lens model parameter space, being an approximate
mass sheet transformation. This family of lens models has not been considered
by the cosmographic analyses. Once added to the model, the cosmographic error
budget should become dependent on stellar kinematics uncertainties. We propose
that a core component coexisting with a cusp could bring the lensing
measurements of H0 to accord with the CMB/LSS value.
