On our Udutu packages, we see an "Exit" button. Clicking that in a popup closes the window, but the Moodle window stays open. If we have the package display in the same window as the Moodle course, the "Exit" button does nothing. Clicking the Moodle "Exit activity" link takes the user back to the course page. Are you packages in a pop-up?
Also, you can remove the exit button from an Udutu package by editing the theme you use. You will find this in under the administration tab in Udutu. If you remove the button, and force the user to click the "Exit activity" link in Moodle, it may trigger the score to push across.