been using iterm for 10 years. Didn't update recently. claude code is the only new factor in my setup. I can visibly predict as i am using claude code when its about to happen (when conversation goes above 200 messages and then uses sub agents leading to somehow infinite rerendering of the message timeline and they seemingly use a html to bash rendering thing because ... ) so yeah maybe you are right iterm is not able to handle those rerendering or maybe the monitor is broken.
I use xterm, and the visual glitch doesn't crash anything, so maybe try that? I suspect though maybe you're using much longer sessions than I do, with the talk of sub agents and all.
I've mostly just been using it for single features and then often just quitting it until I have the next dumb idea to try out.
edit: https://ibb.co/Fbn8Q3pb
that's the 6th