The Burning March Company are a company of Baleros.
The Burning March Company is larger than other companies, exerting protective control over some stretches of land and hiring smaller companies to shore up their numbers. Their organization knows the military subdivision of Battalions (~ several hundred troops; similar to Earth batallions) and Divisions (~ ten thousands of troops, if similar to Earth divisions). This last point may be an author's error. If not, the Burning March is comparable in strength to entire nations from other continents, but not quite big enough for the League of the Great Companies.
When Geneva enlisted with the Raverian Fighters, her company had been hired by the Burning March Company to fight against a local Centaur tribe who had themselves hired the Magehammer Company to occupy a gold mine that the Burning March considered to be under their own protection.
The gold mine was located in the jungle, which hampered the Centaur's tactics most, but also required a slow, bloody campaign on both sides. The local Centaur tribe concentrated to raid the potion supplies of their enemies, which outraged the Burning March and Raverian Fighters. The latter still remained victorious in the engagement, especially when finally a shipment of intact potions arrived at their camp. Magehammer ceded the mining rights to the Burning March (probably after the Centaurs who had made the conflict so bitter, left).
This whole conflict saw the emergence of Geneva Scala as "The Last Light".