The "Clear Completed Tasks" command in the Google Gadget makes them invisible, and we can always see them by using "View completed tasks", if we ever need to remember when the task was completed.
On the other hand, "Purge" in GeeTasks moves the completed tasks to the trash, where we might have all kinds of wrong/blank/misspelled entries that we don't want to see or remember anymore.
And I'm not even sure if the trash gets emptied automatically after a specific number of days or not, but in any case, the trash is the trash, and my completed tasks deserve better than that, especially if I want to remember the day I quit smoking, or the day I bought GeeTasks :)
I think the behaviour of "Clear Completed Tasks" makes more sense, and I hope you'll consider it.