@loobyloo_2 a little clarification needed. What is your final goal with this question, just hide the checkbox, or avoid new users to receive messages on your site?

If it's just hide the checkbox, you need to override the fallback comment form in your skin. In plain english, copy the file /skins_fallback_v6/_item_comment_form.inc.php into your skin directory and delete the section between lines 424 and 428 (it may vary) of the new file: https://github.com/b2evolution/b2evolution/blob/release/6.8.x/skins_fallback_v6/_item_comment_form.inc.php#L424

Both :)

I want to get rid of the option for people to send messages to each other.

Once they have posted their comment, I also want to get rid of everything in this image, apart from the green section
http://ge.tt/9wRMA1k2

@loobyloo_2 did you follow what I mentioned in my latest comment to hide the checkbox from the form?

The first thing you need is to turn off registration after comment, so your users won't be redirected to a registration form after each new comment. That is a per-collection setting, and you can find it by going to: Collection > [your collection] > Features > Comments > Registration of commenters > Register after comment (http://b2evolution.net/man/back-office-reference/collections/collection-features/comment-features/)

Regarding the notifications messages, I think there is no a simple way to get rid of the blue section only (Sending notifications). You could actually hide all notifications, but it will hide the success message too (the green one), which is important.