Kaito and Tenko share minimal interactions with each other throughout Danganronpa V3: Killing Harmony. They appear to mostly have a neutral relationship, and are shown to be willing to work together in dire situations. Although, Tenko will occasionally call Kaito out for what she views as "degenerate male" behavior, just as she does with any other male student.
In Chapter 1, after Kaede gives some encouragement to the group, Kaito suggests that the two of them hug, though Kaede politely declines the offer. Tenko expresses repugnance in Kaito's actions, and accuses him of trying to trick Kaede into pressing her chest up against him. After multiple failed attempts at trying to escape through the Death Road of Despair, a majority of the students are ready to give up, while Kaito and Tenko are among the few who continue to support Kaede, and wish to endure.
After the first and additional motives were presented, Kaito asked Tenko to join his strategy meeting, believing that as the Ultimate Aikido Master, she would be useful when it came to fighting Monokuma. The two were later spotted by Kaede and Shuichi Saihara, heading down to the game room in the basement, along with Angie Yonaga, Gonta Gokuhara, Himiko Yumeno, Maki Harukawa and Rantaro Amami. While down in the basement, Kaito and Tenko find Shuichi and Kaede, and join them in storming the library, believing the mastermind is inside. Tenko asks if she should aikido throw whoever is inside, and Kaito argues that he should be the one to take them down. After entering the library, the group finds Rantaro dead on the floor, causing Tenko to scream, which alerts the other students to the scene. Shuichi manages to calm everyone down, and convinces them to trust each other for the sake of the investigation, in which Kaito and Tenko are the first to agree.
Tenkaito is a rare-pair among the Danganronpa fandom, often overshadowed by Kaito's and Tenko's more popular ship's, such as Tenmiko and Harukaito. Some people might enjoy the ship because both Kaito and Tenko are rather cheerful and are seen as "strong", as Kaito called Tenko to join is strategy meeting, because Kaito thought that Tenko as the Ultimate Aikido Master, would be useful to fight Monokuma.
Because of Tenko's strong hate of men and her canonical attraction to Himiko most of the fanbase sees her as a Lesbian and are critical against het Tenko ships. Tenkaito is often supported by those who see Tenko as bisexual and could see Kaito helping her to understand that not all men are bad.