A friend of mine who is a WWII reenactor & a collector of Scottish insignia sent this to me concerning this badge:

The Highland & Lowland Regiments? Actually they were raised in
the 40's - I'm thinking they were raised in 1940/41 and were
disbanded 1948/49 (I think I've got the dates right...) These were
basically 'Young Soldiers' Regiments - brought in the young guys
and trained them such that when they were of age they would then
be posted to a Highland or Lowland Regiment respectively. Sort of
a way to keep potential Scottish recruits reserved for Scottish
Regiments. As I recall, the Lowland Regiment was primarily
associated with The Royal Scots and the Highland Regiment was
mainly associated with the Black Watch and the Argylls.
So, they're the equivalent of the Officers Training Corps in the UK, and ROTC in the US...

Cheers,

Todd