@aesthr
Thanks for taking the time to write this!
@elduvelle
I also take the approach of focusing on a thing they care about. The feeling "it's just not going through" is shared! Some reply "I know you are right, but I'll continue to use it nevertheless". But it is necessary and useful to explain once and again; like planting a seed, the effect is not immediately visible, and often it simply won't germinate. But sometimes it works.
A minor complaint on "LLMs are simply not capable of producing new knowledge". In mathematics, new knowledge is certainly available through the use of LLMs, and technicalities or stating that it was implicit in the sources won't convince my colleagues. What I do is try to show that the actual cost is overwhelmingly bigger than the benefit.