  We present optical spectropolarimetry of the tidal disruption event (TDE) AT
2019qiz on days $+0$ and $+29$ relative to maximum brightness. Continuum
polarization, which informs the shape of the electron-scattering surface, was
found to be consistent with 0 per cent at peak brightness. On day $+29$, the
continuum polarization rose to $\sim 1$ per cent, making this the first
reported spectropolarimetric evolution of a TDE. These findings are
incompatible with a naked eccentric disc that lacks significant mass outflow.
Instead, the spectropolarimetry paints a picture wherein, at maximum
brightness, high-frequency emission from the accretion disc is reprocessed into
the optical band by a nearly spherical, optically thick, electron-scattering
photosphere located far away from the black hole. We estimate the radius of the
scattering photosphere to be $\sim 100\rm\, au$ at maximum brightness --
significantly larger than the tidal radius ($\sim 1\rm\, au$) and the
thermalisation radius ($\sim 30\rm\, au$) where the optical continuum is
formed. A month later, as the fallback rate drops and the scattering
photosphere recedes, the continuum polarization increases, revealing a
moderately aspherical interior. We also see evidence for smaller-scale density
variations in the scattering photosphere, inferred from the scatter of the data
in the Stokes $q-u$ plane. On day $+29$, the H$\alpha$ emission-line peak is
depolarized to $\sim 0.3$ per cent (compared to $\sim 1$ per cent continuum
polarization), and displays a gradual rise toward the line's redder
wavelengths. This observation indicates the H$\alpha$ line formed near the
electron-scattering radius.
