There is now abundant evidence that the luminosity of the Galactic super-massive black hole (SMBH) has not always been as low as it is nowadays. The observation of varying non-thermal diffuse X-ray emission in molecular complexes in the central 300 pc has been interpreted as delayed reflection of a past illumination by bright outbursts of the SMBH. The observation of different variability timescales of the reflected emission in the Sgr A molecular complex can be well explained if the X-ray emission of at least two distinct and relatively short events (i.e. about 10 years or less) is currently propagating through the region. The number of such events or the presence of a long-duration illumination are open questions. Variability of the reflected emission all over of the central 300 pc, in particular in the 6.4 keV Fe Kα line, can bring strong constraints. To do so we performed a deep scan of the inner 300 pc with XMM-Newton in 2012. Together with all the archive data taken over the course of the mission, and in particular a similar albeit more shallow scan performed in 2000-2001, this allows for a detailed study of variability of the 6.4 keV line emission in the region, which we present here. We show that the overall 6.4 keV emission does not strongly vary on average, but variations are very pronounced on smaller scales. In particular, most regions showing bright reflection emission in 2000-2001 significantly decrease by 2012. We discuss those regions and present newly illuminated features. The absence of bright steady emission argues against the presence of an echo from an event of multi-centennial duration and most, if not all, of the emission can likely be explained by a limited number of relatively short (i.e. up to 10 years) events.