International PPs question

[Hoblin]

In the past performances for European horses, I often see the comment "T. k. h." Is there anyone out there who can teach me what this means? I posted this question to Reddit before this past Breeders' Cup, and to date it's the only thing I've ever asked Reddit that no one seemed to know the answer to. It came up again today in the PPs for Improvise in the 9th at Gulfstream. Please help!!