I thinking about how to do this. The idea is to restore this.element to the state it was in before it went into the task manager. The z-index style property went away, but the element may still be carriying changes to style.MozTransform, MozTransition and opacity. 
I could pass a property bag into leaveTaskManager where the caller can indicate which properties it changed. But elsewhere we are implementing AppWindow.prototype.applyStyle so the TaskManager/TaskCard no longer knows for sure what got changed. 
One idea would be to have a _dirtyStyleProperties = {} on the AppWindow instance, that is reset by enterTaskManager. Then applyStyle (and .transform) can add any properties it changes to this hash, and leaveTaskManager can removeProperty them. That works provided there were no inline style properties we wanted to keep. We could snapshot those and restore them, but it could start to get complicated?