Cannot add any columns because it is a ERP database in which large chunk of data are being added by the thrid party and they will not modify the structure.
I still don't follow. They don't need to know about a new timestamp column to keep using it exactly as they have, and it would be short work to either add it to your database as well, or strip the timestamp data before inserting or updating. The only way this wouldn't work is if you didn't have administrative control of the database. If that was the case, then this solution also wouldn't work:
You can use mysql's update log to see all insert and update commands on a specific table. Check the documentation for details on that.