Setup:
Moodle - 3.10.8 (Build: 20211108)
mod_questionnaire - 3.10.1 (Build - 2021080400)

Replication:
1. Create a course.
2. Turn editing on.
3. Add a questionnaire activity.
4. Go to the questionnaire and click "Add questions".
5. Select "Essay box" and click "Add selected question type".
6. Type in question name and question text. Select Response format as HTML editor.
7. Click "Save".
8. Go back to the course contents page and click on the questionnaire activity.
9. Click "Answer the question".
RESULT: There is no border for the text editor.

Additional: When you click inside the text editor, a border will appear. After you move out focus, border disappears.