The Kurigata is paired with the Shitadome. It is an extension of the scabbard that goes around the Shitadome (ring where the Sageo is rolled up).
All about the Kurigata
For the most basic scabbards, the Kurigata is made of the same wood as the rest of the scabbard (which can still be of good quality) but for the higher quality scabbards you can find Kurigata made of buffalo horn, and they can sometimes even be made of metal alloy.
For a Kurigata made in Japan in the best materials, you should count between 50 and $100. For this reason many choose a wooden Kurigata in the same material as the scabbard.
You have to be careful where the katana is exposed in order to avoid an expansion of the wood and a break between the Kurigata and the Saya which would be unfortunate. Moreover, this often happens with the higher end Kurigata, as it is not made of the same material as the rest of the scabbard, it expands differently and creates a break.
By the way, this is also the reason why we recommend entry level Kurigata to all beginners who want to get into the world of Japanese Swordsmanship.