That sounds to me less of an issue with ChatGPT, and more with having colleagues that don't understand how to engage in reasonable discussion or evaluate information correctly.
ChatGPT is absolutely a symptom here of the underlying problem. Frankly I think it's possible that OP is being too solicitous with these requests. Why does this other team think OP needs a constant input of new ideas? Why do they feel comfortable repeatedly second guessing OP in OP's are of expertise? It sounds like the planning process is totally out of whack. If they were clipping ideas out of a magazine and asking OP to do them it could be just as bad.
And the question was how to get the their coworkers to stop giving copy/pasted ChatGPT technical answers from prompts written by nontechnical people, not how ChatGPT can do a better job.
Good point. Maybe they can invite a discussion where the suggester walks through ChatGPT steps explaining how it is done? Hopefully people aren't so flippant they hammer their keyboard and hit send email. If that's the case, then maybe they need an ego check.
I think my default response would be (regardless of the ChatGPT instructions):
"I looked it over and it doesn't actually work. ChatGPT is good for many high level things but when the specifics get technical, is struggles and invents solutions that don't exist; like a bloom filter. Ask ChaGPT what a bloom filter is."
Sure it's not the tool if you completely ignore 80% of the story. It's cheaper to ban a tool than "hire people who can critically think", as if I ever believed people could intentionally detect that.