  The presence of a debris disc around the Gyr-old solar-type star
$\zeta^2\,\mathrm{Reticuli}$ was suggested by the $\mathit{Spitzer}$ infrared
excess detection. Follow-up observations with $\mathit{Herschel}$/PACS revealed
a double-lobed feature, that displayed asymmetries both in brightness and
position. Therefore, the disc was thought to be edge-on and significantly
eccentric. Here we present ALMA/ACA observations in Band 6 and 7 which
unambiguously reveal that these lobes show no common proper motion with
$\zeta^2\,\mathrm{Reticuli}$. In these observations, no flux has been detected
around $\zeta^2\,\mathrm{Reticuli}$ that exceeds the $3\sigma$ levels. We
conclude that surface brightness upper limits of a debris disc around
$\zeta^2\,\mathrm{Reticuli}$ are $5.7\,\mathrm{\mu Jy/arcsec^2}$ at 1.3 mm, and
$26\,\mathrm{\mu Jy/arcsec^2}$ at 870 microns. Our results overall demonstrate
the capability of the ALMA/ACA to follow-up $\mathit{Herschel}$ observations of
debris discs and clarify the effects of background confusion.
