I guess same thing that happens to any application that sets weird modes. You should use 'reset' command which just emits escape code to reset terminal and terminal emulator hopefully sets everything back correctly.
But not to trust what I just read I've installed kitty and tested it and you can type in the "reset" just fine. I hit a bit of a problem with "Entering" it, as apparently if you have numlock enabled (which I do on login) pressing "Enter" sends escape code: "^[[13;129u", but if you disable numlock it is typed in as per documentation: "0x0d - for the Enter key", which in any ascii table is Carriage Return.
And yes, issuing reset restored normal terminal operation.
Every now and they I'll want to do ^K in Vim and inadvertently hit ⌘K instead, which is fun. (`:redraw!` sorts things back out. Though weirdly it occurs to me that now that the terminal seems to somehow remain in alternate mode…)