I don't know why you are (half) working off the presumption anyone cares about the post-hoc desire of the author.
This isn't tricky at all imo.
Just as if I pasted the text directly, I expect my copying of the content to have the same lifetime as the page I put it on. This is irrespective of anybody's wishes after the fact.
Nobody has the expectation that the text would disappear from my page if copied directly - so why should behavior change in any other case?
The original author of the tweet also has the intent. An unfortunate side effect of having a voice, is that sometimes people will listen and make notes.