  Using MUSE spectra, we investigate how pre-processing and accretion onto a
galaxy cluster affect the integrated stellar population properties of dwarf
early-type galaxies (dEs). We analyze a sample of nine dEs with stellar masses
of $\rm \sim 10^9 \, M_\odot$, which were accreted ($\sim$ 2-3 Gyr ago) onto
the Virgo cluster as members of a massive galaxy group. We derive their stellar
population properties, namely age, metallicity ([M/H]), and the abundance ratio
of $\alpha$ elements ([$\alpha$/Fe]), by fitting observed spectral indices with
a robust, iterative procedure, and infer their star formation history (SFH) by
means of full spectral fitting. We find that these nine dEs are more metal-poor
(at the 2-3$\sigma$ level) and significantly more $\alpha$-enhanced than dEs in
the Virgo and Coma clusters with similar stellar mass, cluster-centric
distance, and infall time. Moreover, for six dEs, we find evidence for a recent
episode of star formation during or right after the time of accretion onto
Virgo. We interpret the high [$\alpha$/Fe] of our sample of dEs as the result
of the previous exposure of these galaxies to an environment hostile to star
formation, and/or the putative short burst of star formation they underwent
after infall into Virgo. Our results suggest that the stellar population
properties of low-mass galaxies may be the result of the combined effect of
pre-processing in galaxy groups and environmental processes (such as
ram-pressure triggering star formation) acting during the early phases of
accretion onto a cluster.
