The battens that hold the wrapping in place need to be removed as you install the new siding. You may be tempted to just install the siding over the battens, but this will lead to long term problems.
Siding installed over the battens will look undulated. The battens would be high spots and the gaps between would be low spots. The result is a wave look to the walls that is only remedied by removing the siding, removing the battens, and installing new siding once again.
Removing battens is very easy. All you need to do is rip it off! The batten will bend easily and snap off at the next screw that holds it in. Be sure to remove the screws as they will also lead to the same wavy look you are trying to avoid.
You don't want to remove all the battens before you begin because the battens do help hold the paper in place until you reach there with the siding.
You can see the torn batten showing at the top of the picture. The dark black lines were where the freshly removed battens were covering the tar paper. The tar paper under the battens was shielded from the sun and never faded.
Removing battens is very easy and can be done incrementally as the siding goes on the tiny house. As the siding reaches the next set of screws, the battens are simply snapped shorter and the screws removed. Then the tar paper was instantly covered by the siding planks, tucking them away behind the siding forever removed from sight.