There is nothing in the data that stores the port so no need to restore data.
Possibly if you have more than one IIS site using the same ip address and the same port there is a conflict and IIS may revert the second site back to port 81. You can use the same ip and port for multiple sites without conflicts if you specify host headers for the domain name so that IIS knows which site is supposed to handle the request. But if you configure 2 sites with the same ip and the same port and don't use host headers there will be conflicts.
Also if you had configured some proxy server or firewall routing so that your customer could use port 80 when it was really running on port 81 then you need to undo that.
Hope it helps,
Joe