These OIA I.D. Badges belong to agents of the Outerworld Investigation Agency (OIA), a modern, military organization formed by two decorated Special Forces officers Lt. Sonya Blade and Major Jax Briggs, dedicated to monitor suspicious activities from other worlds and prevent any future invasions on Earth. It first appeared as a collectible Relic under the name "Sonya's I.D." within the Konquest Mode of Mortal Kombat: Armageddon.
This is Sonya Blade's Outworld Investigation identification badge. Somehow the Tekunin clan gained possession of this item. One of Sektor's cyborg henchmen dropped it after being attacked by the Edenian demigod Taven aboard the Tekunin Warship during the Special Forces' assault against the Tekunin before Sonya retrieved her badge back quickly.
Sonya Blade's I.D. badge later reappeared on her green beret, but in small size in Mortal Kombat vs. DC Universe.