That is the Croce al Valore Militare which was awarded for acts of valour that was undeserving of the Medaglia al Valore Militare. The VEIII monogram represents Vittorio Emanuele III i.e. the Kingdom. The cross was actually instituted by him following WWI.
As of 1947, these crosses carried the RI monogram instead symbolising the republic.
Lilo is correct in saying that the medal would carry a blue ribbon rather than a striped blue and white ribbon seen on the more common Al merito di guerra.
What you have there is a pre 1947 Cross that was re-used (and probably issued after the abdication of the King (in 1946), and the VEIII monogram which symbolises the monarch, was cancelled prior to issue.
There are other versions of these crosses (although I am not sure whether these are only for the Croce al merito di guerra) where the VEIII was actually ground down and the RI stamped instead, clearly showing that the medals were in fact recycled.
I doubt that if that the mark actually represented any division and if issued pre 1947, it is highly unlikely that it would be stamped over the Kings Monogram!!!
Jim :cheers: