Windows ME doesn’t really have an administrator/user type privilege system like NT operating systems. There might be a policy system set up on the box, or it might be the virus/malware generating the message.
If the thing is going to end up connected to the internet, then the first thing I would do is get rid of ME and put Windows 2000 on it. It may take a bit of searching, but you should be able to find an old copy of 2000 somewhere that you can get cheap or free, and 2000 should run on most computers from the ME era. I don’t know if anyone really makes a decent windows 9.x anti-virus these days.
If you can’t get 2000, your second best option would likely be to just wipe the disk and put ME on it again from scratch. It can take days to clean up a badly infected computer, where a re-install only takes hours.