Check the Edit and delete their own posts checkbox.
Note: Unchecking this option will restrict students from editing and deleting their own Discussion replies. This permission affects replies in new discussion topics, discussion replies, and discussions within course groups.
View Student Restriction
When you restrict the ability for students to edit or delete their own replies, students see the Disabled label next to the Edit and Delete options in the Options menu.
Note: If the ability for students to edit or delete their own replies is restricted in a course with Discussions Redesign enabled, the Edit and Delete options do not display in the Options menu.