Word icons with a tiny clock in it

We are seeing a few Word document icons on our server
that have a small clock-looking addition to the Word
icon. It also happens that we can open the file but it
won't let us save changes to the file with the same name
it currently has. It is almost as if it was configured as
a read-only from within the Word file.

So what is the clock on the icon and is that related to
the apparent read only status?

Thanks,
Philip