The ability to edit a stock checks, like many other feature, is governed by the Group Manager permissions. To access this section log into the Reading Cloud management page as an administrator user then select 'Security' from the menu bar at the top of the page and select 'Group Manager' from the drop down menu.
When in Group Manager select/create the group you wish to edit, likely your staff group.
After creating the group/opening the edit window expand the 'Modules' section within the 'Menus' section, select the 'Stock Check' option and switch the 'Visible' and 'Hidden' buttons to the required setting.
If you wish to allow some staff/students to edit a stock check but not everyone, you will need to create a new security group exclusively for those users and grant them the appropriate permissions.