Fix
Short answer: Their role doesn't allow it. Give them a role that can delete the items they need to remove.
Why it happens
On a standalone board:
- Admins and members can create, update, and delete items.
- Initiators can change only the items they created or requested.
- Viewers and restricted members can't delete items.
- Only admins can delete in bulk.
On a board inside an app:
- Edit lets a role update all items but delete only the items it created.
- Manage lets a role update and delete all items.
- External app roles can't get Manage.
How to fix it
On a standalone board:
- Click Manage > Share.
- Change the user's role with Make a member or Make an admin.
See members and roles in a board.
On a board inside an app:
- In the development environment, open the board form and click Share.
- Change the role's permission to Manage.
- Deploy the app. Roles set in development carry over when you deploy.