I just figured it out. The links were part of my background picture. Now, somebody else can figure out how a dozen little .lnk graphics got merged into my background picture.

They look to be the size of small links, but they don't hi-light and clicking on them does nothing.

I have two sets of links on my desktop. One set acts exactly as they should, the other set is a mystery. They appeared spontaneously. I'd blame an upgrade, but I'm not sure.
The other set, the dead...