Hey there,
I am really sorry for the delay of this reply as it is a weekend for us here.
It seems like currently we do not have an option to completely disable this ask button from the backend setting, because it based on the user ACL setting, if the current logged in user doesn't have permission to submit a new discussion post on your site, this ask button will automatically disappeared on the site.
Can you try download my attached file and replace into your current template override file location and see how it goes.
JoomlaFolder/templates/YourCurrentTemplate/html/com_easydiscuss/toolbar/default.php