As easy as wild carrots are to hand weed?
Mowing the hostas may not have killed them... But, it certainly didn't help... These newly emerged leaves were kind of needed to feed the roots.
Probably the best that you can hope for is that the hostas will be reduced in vigour, but will probably come back, if this isn't repeated.
Maybe stop them from mowing the flowers...
or use a different crew...
When we have mowers and string trimmers, many garden crews would rather mow the flower beds than put down the power equipment and pull unwanted plants by hand.