Since we're deciphering code anyway... can I ask if anyone knows what this is?

This is the closest I could find...

"Three small lapel badges of the Royal Arch Purple Degree, that depict a 2½ number within an arch as its emblem. The number 2½ represents the biblical tribes of Reuben, Gad and the half tribe of Manasseh who helped lead the people of Israel across the river Jordan to the Promised Land.
The Royal Arch Purple Degree were founded 1795 at Loughall in County Armagh and continued as part of the Orange Order. They are a Protestant fraternal organisation predominantly based in Northern Ireland but also with many Lodges in Scotland. Some Lodges were also founded in the US and amongst the Commonwealth countries.
The badge's elements are the Royal Arch with the number 2½, an eye, snake and a star."
Thank you! This would make sense. My great-grandmother was Protestant... but the fraternal organisation aspect would be puzzling.