You can decide whether people are allowed to change or remove their own messages after sending.
Go to the Chats page, click the gear icon (Chat settings), and open Message deletion and editing.
Admins are covered by two separate settings, Prevent admins from deleting their own messages and Prevent admins from editing their own messages. These are set by the account holder and apply to every admin in the portal.
Your organization has turned on one of the settings above, which locks messages in place once they are sent.