In the Staff Attributes box are sections labeled Options and Items to Display. In this case, you need to uncheck Display Rests in Empty Measures in the Options section of the SA box; as you said, these are default whole rests and so don't actually exist. Right now, Finale doesn't see any rests to hide, which is why unchecking Rests in the Items to Display section didn't seem to work. (It will, though, as soon as you enter any music with rests on this staff. Better uncheck that box, unless you really don't want to show any rests.)
If unchecking Display Rests in Empty Measures in the SA box didn't work, I'd suspect that the whole rests in this staff are real. Select the Mass Edit tool, click just to the left of the staff to select the entire staff, press Backspace, then try again with the Staff tool.
If this still doesn't work, post the file so that we can take a look at it.
Post Edited (GT) : 10/13/2003 3:44:37 PM GMT