For Itch in general: Itch describes it as:
"This field asks if your project contains the results of generative AI."
You said:
"In a way, I might copy-paste a line of what the generative AI says"
If you are copy-pasting the things an AI generated into your project, then it seems to me that yes, the project contains the results of generative AI.
Itch allows you to specify what parts AI was used in, with these tags:
AI Generated Graphics
AI Generated Sound
AI Generated Text & Dialog
AI Generated Code
Source: https://itch.io/t/4309690/generative-ai-disclosure-tagging