Strange.
I can very clearly hear it in Arrangement view in the set you provided (after clicking "Back to arrangement", since the Session clip was playing).
Then I click Warp twice in the clip (the one in the arrangement) to un-warp and re-warp it, followed by Loop again (since un-warping has canceled the loop). When I drag on the end of the clip in the arrangement to create a couple of loop repeats, the transitions are clean as a whistle, no click. I tried it several times, going back and forth with Undo/Redo, and the difference is obvious in my setup. I'm on Live 12.1.1.
Of course, the clicks shouldn't be there in the first place, since – I can confirm – the loop is indeed seamless.