I have been looking to see if perhaps this is a badge rather that an actual Garter piece.

The Coldstream Guards have the Garter Star as their regimental badge but all views of it seem to show the full star - not just the central element.

I was also wondering if perhaps it was meant to be a more formal "miniature" Garter - in the same way that military medals are worn in miniature on formal evening dress.

I think HM wears it more as a brooch due to its size. It would get lost if worn lower toward the hip like a regular breast star.

Quite perplexing this one...