Emission-line variability studies have the potential to provide key information about the structures of the near-nuclear outflow regions of active galactic nuclei (AGN). Here we present a VLT/Xshooter spectrum of the nucleus of the ULIRG F01004-2237 that was taken in 2018 August, about 8 yr after a major flare in its integrated optical emission. Compared with our WHT/ISIS spectrum from 2015 September, the broad, red wings of the emission lines most closely associated with the flaring event, including He iiλ4686, N iiiλλ4640,4100, and He iλ5876, have substantially declined in flux. In contrast, the broad, blue wings that dominate the [O iii], [Ne iii], [Ne v], and [O i] forbidden lines have increased in flux by a factor 1.4–4.4 (depending on the line). Moreover, the [Fe vii]λ6087 line is detected in the new spectrum for the first time. We interpret these results in terms of a light echo from the outflowing warm gas: the direct emission from the flaring event is continuing to fade, but due to light travel time effects we are only now observing the impact of the flare on the emission from the extended outflow region. Unless the outflow is confined to a small range of angles close to our line of sight, these observations imply that the outflow must be relatively compact (r <50 pc). In terms of the nature of the flare event, we speculate that the properties of the F01004-2237 flare may be the result of a tidal disruption event occurring in an object with pre-existing AGN activity.