The little plastic operating lever on the toilet tank has a left-hand
thread. I cannot think of any good reason for this.

And in passing, the place where I got the replacement had three types that
would fit:

4" plain white plastic - $5.99
4" chromed plastic - $5.09
4/6/8" chromed plastic (cut to fit) - $4.29

Pay more, get less, I suppose....