Using MUSE spectra, we investigate how pre-processing and accretion on to a galaxy cluster affect the integrated stellar population properties of dwarf early-type galaxies (dEs). We analyse a sample of nine dEs with stellar masses of $\rm \sim 10^9 \, M_\odot$, which were accreted (~ 2-3 Gyr ago) on to 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 α elements ([α/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 2-3σ level) and significantly more α-enhanced than dEs in the Virgo and Coma clusters with similar stellar mass, clustercentric 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 on to Virgo. We interpret the high [α/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 on to a cluster.