It still originated in the House, even if the entire text has been replaced by an amendment. The bill signed by the President is labeled either "H.R." or "S", and the Court does not question that designation.

This isn't a clever trick Pelosi and McConnell just came up with. They've been doing it for centuries and its been explicitly approved by the Supreme Court.

In Flint v. Stone Tracy Co. (1911), the Court refused to look beyond the designation of the underlying measure as a House bill. In this case, a House bill that included inheritance tax provisions had been amended by the Senate to contain corporate taxes instead. The Court held that “The bill having properly originated in the House, we perceive no reason in the constitutional provision ... why it may not be amended in the Senate in the manner which it was in this case.”