I’ve never seen that back type either They are normally two pieces. I assume that you already know that the pin goes on a enlisted Army soldiers dress uniform collar.
This type of back (Type V) was introduced during WWII. The ones made at that point had a steel insert holding the pins, where as that piece on ones made post war (and up until 1970) was made of brass. I think that piece on yours is brass, else it would have rusted off. Dating Metallic Insignia: Collar Disks