That is one of the changes in KDE4. Such operations are carried out by a copy / paste plasmoid, and the dialog is the plasmoid's method of providing you information. I do not know of a way to hide the dialog, and I am uncertain that I would want to. On my system, when the operation is finished, the dialog closes automatically and I know it is finished.
You say that it covers the entire screen - on my system, the dialog is a small rectangle in the bottom right corner of my screen (screen resolution is set to 1280x1024 here). If your resolution is different (640x480?), that may be a portion of what is going on . . .
When such a dialog appears, there is a question mark icon in the system tray (main panel) next to the clock. If you are right handed, right click the icon to see if you can access a configuration dialog. Since I have had no trouble with it, I do not know much about it.
If you can not find a resolution, collect as much information about the issue as you can, then make a bug report on the KDE bug tracking system
. You will have to register to make a report, and you should search the existing reports to see if your issue has been reported. If it has, add a comment with the information you have collected. If it has not been reported, add a new report.