Do you have TeaTimer or "SDHelper" enabled in Spybot? If so, then the icon will stay there. It's supposed to be that way.
On Windows XP, the taskbar has a special feature which "covers" the system tray icons that haven't been used for a while (Hide incactive icons). It doesn't mean that they aren't actually running in the background, they are..Windows 2000 doesn't have the option to hide those icons and therefore, all system tray icons are displayed..(Personally, I don't like the "Hide inactive icons" option on XP. I choose to show all icons in the system tray..Of course, I only have two or three there anyway so it's not a big deal.)
That said, if you have either of the "Resident" programs running on Spybot, then the icon needs to be running in the system tray. It's supposed to. If you want to disable TeaTimer or SDHelper and make the icon go away, then open Spybot in the "Advanced" mode, then click on the "Tools" tab on the left side, then click on the "Resident" icon and UNCHECK both boxes on the right side.
Hope this helps.