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It was shown recently that the Fe magnetization reversal in the Fe/MnAs/GaAs(001) epitaxial system, attained by temperature control of the regular stripe pattern of the MnAs alpha- and beta-phases, can also be driven by an ultrashort optical laser pulse. In the present time-resolved scattering experiment, we address the dynamics of the MnAs alpha-beta self-organized stripe pattern induced by a 100 fs optical laser pulse, using as a probe the XUV radiation from the FERMI free-electron laser. We observe a loss in the diffraction intensity from the ordered alpha-beta stripes that occurs at two characteristic timescales in the range of similar to 10(-12) and similar to 10(-10) s. We associate the first intensity drop with ultrafast electron-lattice energy exchange processes within the laser-MnAs interaction volume and the second with thermal diffusion towards the MnAs/GaAs interface. With the support of model calculations, the observed dynamics are interpreted in terms of the formation of a laterally homogeneous MnAs overlayer, the thickness of which evolves in time, correlating the MnAs microstructure dynamics with the Fe magnetization response.