After my old G5 IMac hard drive failed and was replaced, 4 months later the graphics chip failed.

I bought a new IMac with Lion and proceeded to download all the stuff that an expert was able to recover from my original failed hard drive.

When I had downloaded my photos to IPhoto, the icon of the downloaded photos remained on the desktop. Nothing I tried would get rid of it and I ended up with several aliases in the Trash, which took an age to empty. Dragging the icon from the desktop into the Trash stopped IPhoto from opening any photos. Dragging the icon into IPhoto left an alias on the desktop.

When I did this previously with my new hard drive everything worked fine with no icon remaining on the desktop. What action, if any, should I have taken so that it disappeared after downloading to IPhoto?