I interpret it that you are not allowed to remove the AGPL 3.0 license / copyright notice. Not the payment nag notice.
I know these are no truth-telling toys, but this is what Gemini Pro says:
"- You can fork the project.
- You can remove the payment reminders/nagging feature.
- You can make this modified version available for others to deploy.
Crucially, you must do so under the terms of the AGPL 3.0, including making the complete source code of your modified version available to those who use or deploy it.
The original author chose the AGPL 3.0, which grants these freedoms. While they can request payment or add reminders in their version, the license itself allows users to modify and share those modifications. Your actions would be a demonstration of the freedoms provided by the license."