Keeping in line with the 2010 version of the story, when Hatter yells at Chessur about betraying them when the Jabberwocky started to attack, I believe Hatter wasn’t just angry at Chessur but also at himself. While his primary job when the Jabberwocky started attacking was protecting the Queen at all costs, he could perhaps have gone back and saved a few more of his clan, but he was too scared to do so, resulting, unfortunately, in his being the last of the Hightopps. By blaming Chessur, Hatter can divert the blame he feels on a daily basis towards himself for not going that extra mile to help his clan away every once in a while.
He does care for the mischievous cat, finding that good friends are hard to find nowadays and during the time under Iracebeth’s rule. Without the feline’s help, he would have definitely found his head detached from his body and for that he is grateful towards Chessur. He’s even thought about making a hat for Chess if only to persuade the cat from trying to steal his own.