Hey there,

I am really sorry for the delay of this reply as it is a weekend for us here.

I think this work around solution can be meet your current requirement :

1. Create logout menu item and set the access to registered, then set the redirection to your site homepage, you can refer my attached screenshot, mean this logout menu item only appear on registered user only.

2. Apply this following custom css into your site backend > Easydiscuss > theme > custom css , so it will disappear this logout button from the Easydiscuss toolbar dropdown section.

body #ed .ed-toolbar [data-ed-toolbar-logout] {

    display: none;

}

If you still want user click that logout button from the toolbar dropdown, then you have to modify this on this PHP file -> JoomlaFolder/administrator/components/com_easydiscuss/includes/router.php

Add this following code into this section, you can refer my 3rd screenshot below.

$redirect = JURI::root();