This chapter of the guide to GreedFall has the walkthrough for Camp of the Ordo Luminis side quest.
Where to start the quest?: Complete Face to Face with the Demon main mission.
You can complete this quest in two ways. You can go to Eseld and talk to her about rescuing the prisoners or go the Mother Cardinal.
Conversation with Mother Cardinal - after a conversation with the woman, go to the barracks, talk to the quartermaster and recruit a group of knights to help you. Then, go to the meeting place in San Matheus and attack the camp together with the allies. Save the prisoners, kill all the inquisitors, find evidence in the chambers - after that, talk to the allies and report everything to the Mother Cardinal. You will get +1 reputation with Theleme. Go now Derdre and tell her everything - she is displeased, you get -1 reputation with the Naut.
Conversation with Eseld - convince the woman by using, for example, charisma, to make her join the battle. The assault looks exactly the same as in the description above - free the prisoners, defeat everyone and go to the Mother Cardinal. You get -2 reputation with Theleme. This will complete the quest.
Regardless of the choice, you will also get +4 reputations with the Naut and 1,900 XP.