What does Allow Invisible Connection Attempts mean
The ability to allow an application to make an Invisible Connection Attempt, is part of the Application Monitor rule configuration.
If you select this option, you are essentially telling CFP, that you fully trust the application and would rather not receive alerts from the application.
Question: What is an “invisible application”?
Answer: An invisible application is one that is starting itself, or is starting without interaction from the system. An example…
Using Firefox as a browser, starting from a desktop shortcut (or toolbar, or whatever): The parent is explorer.exe, as the windows shell. However, when Firefox updates, it restarts itself after the update. Now it’s parent is firefox.exe, and it is an invisible application, since the user did not specifically click on something to start the application. We did originally, but after the update it restarted itself. Invisible.
A lot of auto-update modules (for antivirus, Windows, etc) are invisible. They start themselves; the user does not.
You don’t have invisible parents, only invisible applications.
LM
Invisible parents are the problem. Can you figure out how to make my mum silent?
Ewen 
Yes. The child needs to mature first.