It’s a tophat. It came into fashion in the early 1800s and had pretty much run it’s course by 1930 or so. So in this comic it’s kind of at the end of the run. Imagine someone showing up with layered polos and an Ed Hardy trucker hat and you get the idea. My own wife likes me to wear bowties out and I personally think they look stupid. And I hate to tie them. Who even wears them out anymore? _me.

Eta: I notice that there is a texture difference between ET and the man in the back also wearing a topper. I wonder if it’s supposed to suggest that the one in the back is silk and True’s is beaver felt? Or maybe there is something else that I’m missing in the context.

The man is saying Everett’s hat is old if it’s from before the war. Everett still wears the hat because his wife likes it.