The first thing he changed was the story about how Meta died. Arit killed Meta, but Mark told Greg that Meta was already dead when he came here to see the Calamity Class. That way, Greg wouldn't have too many questions about how Meta died and Mark wouldn't have to tell too many lies.
When you lie too much, your stories start to make less sense.
Mark also kept Arit's involvement in his injuries out of the story, and he was able to formulate a good enough response to fool Greg into thinking that everything here was caused by only the Anima and Mark, without involving Arit at all!
Pat's just a tundere