Answered elsewhere, but, to be complete, clicking the X is a rule change, so you then need to save the "new" rule to the Twine by clicking the "Save Rule" button. I have suggested to the Twine team that they need to make the web interface more useful, such as, greying out the "Save Rule" button once it has been saved, and un-greying it after any change, so that users would know they have to save again. This is very much a work in progress.
I've tried all of the above and various other combinations, but I cannot get the rule deleted. It disappears from the page, but comes back after a refresh. Or a re-login.
Same thing here. I can't delete rules from my Twine. The solution I found was to replace the rule with one that does nothing, and that seems to solve it for now.
Answers
I have suggested to the Twine team that they need to make the web interface more useful, such as, greying out the "Save Rule" button once it has been saved, and un-greying it after any change, so that users would know they have to save again.
This is very much a work in progress.