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You're assuming you have copyright on your tweets which is unlikely as this essay lays out: http://www.canyoucopyrightatweet.com/

That essay points out plainly that some, just not most, tweets are possibly copyrightable. Your parent's point stands.

I think it says that it's highly theoretical there would be one that is copyrightable (and that you would need to register copyright on a tweet before being able to take action). My point was that therefore it's unlikely you'd consider what they're doing copyright infringement, but sure it's "possible". Unethical is another question entirely :-)

This very well seems like copyright infringement. They also don't post a DMCA contact.

Is this not similar to how some media report about an event and include a tweet that has been since deleted. This just being done on a much broader scale.

It's in the public domain... it's open for grabs.