Context. X-ray quasi-periodic eruptions (QPEs) are repeating, high-amplitude, soft X-ray bursts observed from the nuclei of a dozen nearby low-mass galaxies. Their origin remains a major puzzle in the physics of accretion variability. Observational data indicate that X-ray and/or optical tidal disruption events (TDEs) may precede QPE detections. Although both kinds of outburst are driven by supermassive black holes, they are more frequently detected in faded active galactic nuclei (AGNs), when the TDE is not happening in a dormant galaxy. In the case of the QPE discovery source, GSN 069, observations and simulations have revealed evidence of past nuclear activity, although it remains debated whether this activity arose from a past AGN phase or from an enhanced TDE rate. Aims. We investigated the origin of the past nuclear activity in GSN 069. Methods. Past AGN activity imprints detectable polarization in optical light, due to the expected delay between direct and scattered light. On 6 September 2019, we targeted GSN 069 with VLT/FORS2 in both imaging polarimetry and spectropolarimetry modes so that its optical polarization could be investigated while the first detected QPE phase was still active. Results. We measured a rising polarization, from ∼0% to ∼1.5%, as moving away from the nucleus of GSN 069. This rise is probed to be intrinsic to the central engine, confirming the already detected extended emission line region (EELR) by integral field unit data. Conclusions. The increasing radial polarization demonstrates a switched-off nucleus. The polarization angle traces an axis aligned with elongated [OIII], [NII], and Hα gas distributions, revealing an EELR that may be consistent with relic polarization cones, therefore suggesting the presence of a torus-like structure in the past. Thus, optical polarization echoes geometrically favor a faded AGN as the origin of the EELR rather than a past elevated TDE rate, although the latter cannot be excluded.