If you move the items to the 'Removed' status, from there you will be able to move them back to the 'New' status.
If moving things from Approved to New is a common occurrence for you, consider adding a transition directly from Approved to New by editing the advance project settings xml available via the Settings Tab > Project Settings > Advanced Settings. More information available here: Editing TeamPulse Project Settings
However, since you are syncing with TFS, you would also need to adjust your TFS project's process template to include the transition. This is a bit more involved, and you will not be able to sync if your TFS and TeamPulse project statuses and transitions do not match.
the Telerik team