Wikipedia says alveolar clicks are found only in Africa/Australia, which isn’t true at all.
For instance, there’s the one usually done twice in rapid succession with the tongue against the upper side teeth/gums – to “gee up” a horse, indicate “mock-conspiratorial” agreement, etc.
So far as I know, we don’t even attempt an onomatopoeic written representation of that one, but the one formed by suction against the back of the front teeth/palate is normally written as either “tut” or “tsk”. Sometimes people actually say “tut” or “tut-tut” (presumably, influenced by the written form).
But I’ve never heard anybody say anything remotely resembling “tsk”. So where does the “k” come from in that written representation?
Presumably for the same reason that dogs barking don’t say “woof”. “Tsk” is a phonetic sound that corresponds roughly to the tutting sound. I note that my tongue and teeth end up in roughly the same part of my mouth when I say “tsk” as when I tut, whereas saying “tut” gives a totally different mouth shape.