How to get rid of a zip file icon on the desktop?

My dad has a G4, 10.4.11. He has a zip file icon on his desktop, and we can't figure out how to get rid of it. We had originally clicked on it to see what was in it, but what happens is that we see it open--the screen expands in a split-second as if an image is opening, but then we don't see anything new. Then, when we try to empty the trash with this icon in it, we get a message that we can't empty the trash because the zip file is in use.

Seems to me that it indeed is in use, as it seemed we opened up the zip file when we clicked on it. But as I said, we didn't see anything open up. We also can't figure out how to close it if it is indeed open.

Help! We just want to get rid of this zip icon. Thanks.