  We analysed the high-resolution (up to $\sim$0.2") ALMA CO (2-1) and 1.3 mm
dust continuum data of eight gas-rich post-starburst galaxies (PSBs) in the
local Universe, six of which had been studied by Smercina et al. (2022). In
contrast to this study reporting the detections of extraordinarily compact
(i.e., unresolved) reservoirs of molecular gas in the six PSBs, our
visibility-plane analysis resolves the CO (2-1) emission in all eight PSBs with
effective radii ($R_\mathrm{e,CO}$) of $0.8_{-0.4}^{+0.9}$ kpc, typically
consisting of gaseous components at both circumnuclear and extended disc
scales. With this new analysis, we find that the CO sizes of gas-rich PSBs are
compact with respect to their stellar sizes (median ratio
$=0.43_{-0.21}^{+0.27}$), but comparable to the sizes of the gas discs seen in
local luminous infrared galaxies (LIRGs) and early-type galaxies. We also find
that the CO-to-stellar size ratio of gas-rich PSBs is potentially correlated
with the gas depletion time scale, placing them as transitional objects between
LIRGs and early-type galaxies from an evolutionary perspective. Finally, the
star formation efficiency of the observed PSBs appear consistent with those of
star-forming galaxies on the Kennicutt-Schmidt relation, showing no sign of
suppressed star formation from turbulent heating.
