From my understanding scraping a public website you'd otherwise have access to is legal in the US. However, re-hosting that scrapped copyright content, particularly if it isn't transformative/fair-use (inc. only partial content) is very much either violates copyright, or best case is legally a gray area.
Google got dragged into court for exactly this, and they were summarizing/snipping, so they had a fair-use argument to make. This is a 1:1 reproduction of the content, so the legal arguments on fair-use would be harder to make I suspect.
I've personally used XCancel, and I really like it, but stepping back legally they're on shaky ground if Twitter decides to stop it.
AFAIK, to date Twitter hasn't required its users agree to a copyright assignment or an exclusive license to the content of their tweets, so it wouldn't be a copyright suit. Twitter wouldn't have standing to bring suit, as that would be reserved for the actual copyright holders, i.e. Twitter's userbase.
Google got dragged into court for exactly this, and they were summarizing/snipping, so they had a fair-use argument to make. This is a 1:1 reproduction of the content, so the legal arguments on fair-use would be harder to make I suspect.
I've personally used XCancel, and I really like it, but stepping back legally they're on shaky ground if Twitter decides to stop it.