I need access to the Twitter Ultimate copy in order to test it. You can share its .zip via DropBox or GoogleDrive with support [at-sign] role-editor.com
I install such products locally and use for the testing/investigation purpose only.
So this menu item is available to any user with the deprecated ‘level_1’ capability.
Solution 1st: edit ‘twitter_ultimate.php’ file and replace 1 with ‘manage_options’ or other user capability on your choice.
Another solution – revoke level_1 deprecated capability from a role for which you wish to prohibit access to this menu item. User with such role can disappear from the list of authors at the post editor page though (more information).