  A possible interaction between cold dark matter and dark energy,
corresponding to a well-known interacting dark energy model discussed in the
literature within the context of resolving the Hubble tension, has been
investigated. We put constraints on it in a novel way, by creating new
likelihoods with an analytical marginalization over the Hubble parameter $H_0$,
the sound horizon $r_d$, and the supernova absolute magnitude $M_B$. Our aim is
to investigate the impacts on the coupling parameter of the interacting model,
$\xi$, and the equation of state of dark energy $w$ and the matter density
parameter $\Omega_{m,0}$. The late-time cosmological probes used in our
analysis include the PantheonPlus (calibrated and uncalibrated), Cosmic
Chronometers, and Baryon Acoustic Oscillations samples and the Pantheon for
comparison. Through various combinations of these datasets, we demonstrate
hints of up to $2\sigma$ deviation from the standard $\Lambda$ cold dark matter
model.
