According to Jim Recap: The Cat Came Back
Andy, Dana and Jim are on their way to a football game when Cheryl calls with the news that her cat has died. So reluctantly they head back home to console her. Needless to say, Jim isn't very good at it. As it turns out, it's not just because he is insensitive (though that's a part of it) - he's just not a cat person.
Cheryl asks him to bury the cat, but since the ground is frozen, he instead puts the cat in the freezer and heads to the game. Cheryl, unfortunately, finds the cat and isn't too happy about it, and let's just say she shares her unhappiness with Jim.
He can't understand - to say the least - and it all just goes downhill from there.
Jim buys her a dog that he names Gary Sinise, which is seen only rarely in future episodes. He does make up for things by playing a harmonica dirge and singing Amazing Grace with Andy and Dana in the backyard after burying the cat, even when Cheryl had about given up on him.
While Cheryl was upset about losing the cat, but a lot of it stemmed from the fact not that she lost the cat, but that it was her last memory of her life prior to her life with Jim and the family - that's a lot of trauma in a little cat.
As a piece of trivia, the cat's name (Mr. Feeney) came from her former boyfriend, which comes out, but isn't told to Jim. One of the show's writers and producers is named David Feeney, but he didn't seem to have anything to do with this episode - so chances are it's just a coincidence.
