The mistaken phrase is next:
should we tell him about the argument?
¿deberíamos hablarles* de la pelea?
Correct: ¿deberíamos hablarle de la pelea?
It must be ‘hablarle’ cuz it’s the singular of third person not plural.
¿deberíamos hablarles de la pelea?
should we tell them about the argument?
As you can see, this works if there are more than one person to tell about the argument. It must be plural in this case.