Why do this?
While it may be an annoyance to see that address, remember that at some offices a log of incoming non port 80 traffic is logged. So you'll need to find that log as well.
Be sure to search the registry too.
I've used Remote Desktop from my workplace to remote into my home PC. Whenever I go back to the remote desktop on my work computer it has my home IP address stored in it. Is there a way to clear the settings? I've tried highlighting the IP address and hitting the delete key and deleting the default.rdp file but my home IP address is still there.