hc, I have checked on a couple of sites, and it appears that badgers are not especially frightened of humans, so the scent of them is unlikely to deter the badgers from coming into a garden.
Badgers are timid creatures, and will be scared by noise and movement, but not by scent, which, it appears, they will simply ignore.
Why not try bright external lights with motion sensers on them? We live very near to a rural area and see no wild animals in the garden at night - the only things that set off the lights are the neighbour's cats, which have learned to ignore the lights completely.