Currently the style code that controls the background color defined in inline CSS code.
In the EAN plugin if you open “includes/ean-functions.php” and go to line 426 (could be different since my copy has changes in it).
You should see a line within the mail_head() function:
$head = '<div style="width:700px;border:1px solid #EEEDED;background:#F6F5F5;padding:10px 20px;font-family:Arial,Verdana;">';
Here you can change the background color to use an image instead.
Refer to the following page if you are not familiar with CSS and setting background image:
https://www.w3schools.com/css/css_background.asp
^^ Please note that in the above page the code refers to the image in current directory where the file you are editing is at. So, if you were to just do something like background-image:url('test.jpg'); then ean-functions.php would be looking for that image in the includes folder.
I’d recommend placing the image in the images folder within the easy-automatic-newsletter folder.
Your code should then look something along the lines of:
...
$head = '<div style="width:700px;border:1px solid #EEEDED;background-image: url(https://mouyios.com/wp-content/plugins/easy-automatic-newsletter/images/on.png);padding:10px 20px;font-family:Arial,Verdana;">';
...
