The word moderaban is the imperfect form of moderar in the third person plural.
See the full moderar conjugation

moderar

Los dos partidos se acusaban, y los dos moderaban su lenguaje para evitar enfrentamientos.
The two parties flung accusations at each other, then moderated their language to avoid confrontations.
Los iraníes creyeron que sin importar qué hicieran, aún si moderaban sus políticas, EE.UU. seguiría procurando el aislamiento de Irán, y la única manera en que Irán podía obligar a Washington a cambiar su postura era imponiendo un costo a EE.UU. por no hacerlo.
The Iranians believed that whatever they did, even if they moderated their policies, the U.S. would continue to seek Iran's isolation, and the only way Iran could compel Washington to change its position was by imposing a cost on the U.S. if it didn't.
Las personas que moderaban el debate nos hicieron preguntas injustas.
The people who moderated the debate asked us unfair questions.
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