In "We Branded Each and Every Animal," why do they brand the cattle, and how is it accomplished?

Rosario is concerned that at "The Fort," they will confiscate the cattle because they are not legally his property. Liz wants to keep the cattle, so she suggests that they brand them with the sign of the estancia that she and Oscar were hired to oversee. It is China Iron who figures out how to fashion a branding iron from a piece of metal from the wagon.