I am currently using Elgg 2.3.7 and html_email_handler 4.0.4 for my website. We would like remove the gray box around the email message and modify the content of the message as well. 

Is it possible to override the email body of this plugin? If yes, how can I achieve this?

Thank you in advance!

You can overrule the html layout by using this view https://github.com/ColdTrick/html_email_handler/blob/v4.0.4/views/default/html_email_handler/notification/body.php

And the CSS is handled in https://github.com/ColdTrick/html_email_handler/blob/v4.0.4/views/default/css/html_email_handler/notification.php

http://learn.elgg.org/en/stable/guides/views.html