Approved course request can only be removed within onRecord with the list Requests and recommendations or within schedule maker. Please review Can I remove course requests in bulk? to complete that task. 

To remove the course request with the Requests and recommendations list:
  1. Login and Navigate to onRecord 
  2. Lists >  Requests and recommendations
  3. Enter the student's name in the Find in list search
  4. Click on the three horizontal dots on left of the student's name
  5. Select edit requests and recommendations
  6. Click on the Trashcan icon for the request you would like to remove. 
  7. Press apply changes