Time-delay distance scales as $1/H_0$

For all real $c$, $\Omega_m$, $z_{\rm lens}$, $z_s$ and all nonzero $H_0$, $H_0'$, the time-delay distance of Eq. (1) satisfies

So $H_0 D_{\Delta t}$ does not depend on $H_0$: the time-delay distance is inversely proportional to the Hubble constant, with the remaining cosmological dependence ($\Omega_m$) entering only through the proportionality factor. This is the precise sense in which $D_{\Delta t}$ is "primarily sensitive to $H_0$, with weak dependence on other cosmological parameters".