Mozilla Thunderbird displays an alert message when a new message arrives. The alert is as shown in the below picture.
Thunderbird also provides option to disable the above alert message. This can be done using the Tools –> Options menu.
Click the Tools menu and select options from the list of available menu list.
To disable the display of new message alert, in the following options window, navigate to When new messages arrive section and un tick the check box with label as Show an alert.
After making the changes, click OK button to save the changes.