"This mysterious tool was made using forgotten ancient technology. Place it by opening your pouch and registering your current location as a travel gate."
The Travel Medallion is a Key Item found in Breath of the Wild with The Master Trials DLC. It allows Link to create a fast-travel point which he can warp to at will. This works very similarly to how Link can warp to the many Shrines across Hyrule.
The Medallion establishes a warp point where Link is currently standing, so that Link can return to that point from afar. However, Link cannot place the warp point until he reaches said destination by foot in the first place. The warp point cannot be placed if Link is mid-air, scaling or not on solid ground.
Given the terrain and inclination of the land, the medallion's marker may not appear under Link, but will show up on the map.
The Medallion is available by accessing the Inventory Menu using the (+) button; as such, it cannot be accessed through the Map Menu with the (-) button, as that only gives Link access to the pre-established warp point.
EX Teleportation Rumors!
- Main article: EX Teleportation Rumors!
The Travel Medallion is part of the EX Teleportation Rumors! side quest that is unlocked when The Master Trials DLC is activated. The quest leads Link to the South Akkala Stable, where he will find the Super Rumor Mill V2 book. The book will talk about the Travel Medallion and indicates it is located beneath a labyrinth in northeast Akkala.
The rumor is referring to the basement of Lomei Labyrinth Island, located at the far northeast corner of the map. Link will first need to complete the Trial of the Labyrinth shrine quest in order to find the Tu Ka'loh Shrine. After completing the quest, he will gain access to the basement of the shrine (a hole in the floor directly south of the shrine on the same floor; burning some thorns may be needed to see it). Drop down to the basement through the wind geyser. Beware of the many Guardian Stalkers and Decayed Guardians in the area. The treasure chest at the south end of the map contains the Travel Medallion. A Diamond Circlet is in the middle chest.