Copy a rectengular block into primary selection from within screen session

If you are on a remote machine in a screen session you can Enter the "copy-mode" by

Ctrl+a+ESC and then use Space and the arrow keys to do a normal selection.

Now you can use a small c to set the left margin, and capital C to set the right margin then press Space again to copy the selection into the screen buffer (as described in the screen manual)

How can you get the selected block into your primary selection or clipboard on your local machine to use it in another GUI application on your desktop?