I found a way to disable the annouing notifications
Open "HP Client Security"
Select "Password Manager"
At the bottom, select the link for "Browser Integration"
Now you get a list of the browsers HP thinks they support
Expand the section for the browser you want to shut up notifications for
Uncheck the checkbox at the bottom that says "Show Integration problem notifications"
One thing is that this is annoying if you don't want to cativate the plugin. A much more serious thing is that the plugin they have for Chrome uses technology that Chrome does no longer support for the plugins, so it is not possible to activate the plugin at all - even if you would want it!