I’m not seeing ‘L-22’ on the back. It’s marked ‘L.I.G.I.’ which stands for ‘Lordship Industries Government Inspected.’
The company was founded in New York in 1948 as ‘His Lordship Products Inc.’ using a ‘H.L.P.’ mark and changed name to Lordship Industries using the L.I. mark from around 1973. The addition of the ‘G.I.’ (alongside both maker marks) was a U.S. government requirement from the late 1960s onwards. The company officially lost its government contract in 1996 following the illegal sale of medals, which they also produced.
So that gives you a timeframe between about 1973 and 1996 but I don’t believe the badges themselves carried any date coding. The boxes in which they were issued did: month and year as either contract date or fiscal year.
The badge was worn on the left side of the collar by three ratings: Hospital Apprentice, Hospital Apprentice First Class, and Hospital Steward (Chief Petty Officer) in both the U.S. Navy and Marine Corps. Hospital corpsmen served in shore establishments such as naval hospitals and clinics providing medical care to sailors and their families; and aboard ships and submarines as the primary medical caregivers for sailors while underway. They also serve as battlefield corpsmen with the Marine Corps, rendering emergency medical treatment, including initial treatment in a combat environment. Further, they provide medical care to the Fleet Marine Force, SEAL and Seabee units, and at isolated duty stations where no medical officer is available.