Hiki Otoshi means to pull down.
This Tanto Dori teaches you first of all Nami Gaeshi - to return and counter instantly in one flow before the attacker has a chance to stab again.
Second is control and manipulation of the elbow joint and shoulder which enables you to get in position to throw.
This is the one and only technique from the series where you can see that the Saya is used.
Back in 2013 I shot some pictures on how to use the Saya. In Hiki Otoshi Dori use the Saya to attack the chin and setup your stab.
There are different ways to use it. For example: stab, block, catch and thow: