The poltergeist looped the cord around the interloper's neck. He could hear the other ghost screaming at him, yelling at him to stop. He tightened the cord. He wanted her to leave as much as the humans. This was his house. Everybody else had to go.
When the other one came in and tried to pull it off, he laughed. Then when he flung that useless bag in the wall, he decided to pretend to leave. Make them feel safe and he would get them later. The other ghost could feel his plan. He laughed at her. She couldn't stop him.