If an analyst visit an Incident or any other type of record, by default they can view/use the edit button so you can change the record and then save.
To disable this functionality, login to CA Service Desk Manager (with an administrator userid) and select Administration tab => Select Options Manager => Search "edit%" => Select from the list you get: option "edit_inactive" => click at EDIT button => INSTALL.
Then stop and Restart SDM.
Now when someone tries to EDIT an inactive ticket, they will get message:
AHD05229:No permission to update an inactive record.