When a story is split the one marked [Continued] is the original story. That story is moved to the next iteration. The one marked [Unfinished] is created as a placeholder in the old iteration for historical purposes. Generally any completed tasks will be moved to the [Unfinished] story and incomplete tasks would also be moved with the [Continued] Story.
When Items have been added to the timesheet they will remain unless manually removed or changed. We don’t currently make automated changes to these entries unless they are things like updates to names, or if an item is deleted. Even if it is deleted it will just turn grey rather than be removed.
Therefore, since the hours for the task was entered on the [Continued] story they will still be displayed on that story, even though its current parent may be the [Unfinished] story. This makes sure that the timesheet is an accurate report of the work when it was done.