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 $3sigma$ 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.
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