The scroll icon is the AppleScript icon. In Word, you will see the same icon next to Help in the menu bar. You could check that menu to see if anything is listed...nothing is there by default. Word stores installed AppleScripts and Automator Actions in ~/Documents/Microsoft User Data/Word Script Menus. Maybe you added one at some point, which i executing when you close Word? Also, that icon does appear normally when quitting Word, as there are Microsoft scripts that run to save the Normal template and settings/preferences. But, it should only show for a second or so.
Another possible solution, would be to totally trash the ~/Documents/Microsoft User Data folder. Unless you use Entourage for email, or have any Office customizations, this folder can be safely deleted and it will be recreated the next time you launch one of the Office apps.
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