The proper procedure isn't for a bill that's not a bill to raise revenue to start in the House.
Any bill that's not a spending bill can start in either the House or Senate.
They have been following the proper way to pass a non spending bill.
Read below and pay attention to the last paragraph.
I was taught this in Elementary School in the late 1960s. I'm surprised that people today don't know what's actually in the Constitution.
Submitting a Bill
Bills originate from several different sources, but primarily from individual members of Congress. In addition, bills might be brought to a member by a constituent or by a group of constituents; a bill can be submitted to a member of Congress by one or more state legislatures; or the President or his administration might suggest a bill.
However it is brought to the attention of a member, it must be submitted for consideration by the member. In the House, Representatives need merely drop a copy of a bill into a bin specifically placed to receive new bills. In the Senate, the bill is given to a clerk at the President's desk.
Bills can be introduced in either house, though as noted above, a bill must eventually pass both houses to become law. The exception to this is that bills for raising revenue must originate in the House, and never in the Senate.
https://www.usconstitution.net/consttop_law.html