How did he kill the hotel woman he slept with?

Vulcan neck pinch.

i think the answer is that because of the rating standards of the time they wouldn't show something graphic like the person struggling in death throes for an extended time. so they had a somewhat lame scene where they leave it to the imagination and you assume he did some kind of special ninja assassin move that produces instant death with no sound.

My first thought was whether he had hidden on him some poisoned needle, or tiny capsule containing a dermally-administered poison or something. The scene had my head scratching too.

If it was something else like what others here suggest, they could have shown it being a bit of a struggle at least--still quiet enough that the house staff wouldn't hear anything. This would have been more believable. But it was only a minor flaw in an otherwise very well-executed story.


Understanding is a three-edged sword.

I wondered that too. The obvious answer is that he strangled her but it was silent and with no visible movement other than his kiss.