Hello Giora,
You need to disable Joomla's plugin and enabled our "System - Admin Tools Joomla! Update Email" plugin. It does the same thing but it also uses the secret URL parameter.
You may wonder, why did we have to copy Joomla's update notification plugin. In fact, it was the other way around. I saw that our clients who were using the Admin Tools Joomla! Update Email plugin tended to have more up to date sites and had much fewer incidents of security issues. So I convinced the Joomla! project to include that plugin inside Joomla! itself. The requirement for accepting my plugin was to remove any code that was specific to my own software. So we had to remove the code which allowed us to add the secret URL parameter. That's how we ended up with two plugins, the basic version included with Joomla! itself and the smarter version included with Admin Tools.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!