Air carrier ground personnel reported there was miscommunication with a passenger who had checked a baggage at the gate that contained a lithium-ion battery. This event; along with the flight crew having an issue with something missing in the cabin; led to a delay.

Narrative

We work in the airline industry where uncontrollable things happen. Aircraft X was ready to close; on time; when a passenger identified that her gate check which was already taken downstairs had a lithium battery in it. She did not speak English. The agents working the flight along with my trainee were speaking with her. We come to find out it's not just a battery but a battery bank to power the lack of electricity in her final destination of ZZZ1. So VERY big back-up battery.This had to be removed. The passenger spoke NO English and didn't understand until later what exactly was being asked of her regarding batteries because her son had told her if she was asked about it to say yes. She didn't initially understand the question.This was getting into no impact for a STAR flight which was ALL that Operations Person A was concerned about. Not the safety of the passengers should a fire happen midflight... impact. Is impact and a 2-minute delay worth a full flight of lives?There were other issues with the flight where Person A was looking to blame the agents for unpredictable stuff yet again. We were training and had gone to close. By this time; there are four people on the jetway; the two working the flight the trainer and the trainee. Everything was good to close. The trainee went to go close the door and the Flight Attendant said wait no no. The person was talking to the Captain about something that was missing in the last row that they did not tell us what it was. They were trying to see if it was a no go item or not. The person was speaking with the Captain and as soon as they were done; I asked if they were ready to close and we closed the door immediately. Operations is more concerned that the agents working the flight were starting to walk up when the doors were supposed to be closing. They started once the gust lock was pushed - but we got the no no from the crew.They are putting stressful blame on Customer Service because the agents went up; more concerned with who to place the blame on and get them in trouble rather than any sort of accuracy or safety. No one knew about this until door closing. Whether the two agents were there or not would not have changed the outcome?Once again; more concern was put on the fact of this being a STAR flight than the safety of the passengers flying to ZZZ and the safety of the agents who are going to be under severe stress for uncontrollable things that were not their fault that will be blamed on them for Operations fishing for a way to twist it.