Article 5 of the US Constitution requires 2/3 of each house of Congress to approve an amendment before Congress can submit it to the states for ratification.
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution.
In the 1978 ERA deadline extension, only majority votes were used to extend the deadline to 1982.
In 1978, the House and Senate, acting by simple majorities, adopted a resolution extending the deadline for the ERA’s ratification. 92 Stat. at 3799.
The votes in the House and Senate were 233–189 and 60–36. 124 Cong. Rec. 26264, 34314 (1978).
https://www.justice.gov/olc/file/1232501/download p.8 (PDF)
One of the questions answered in Idaho vs Freeman was whether the simple majority of each house of Congress was sufficient, or if a 2/3 majority was required.
In any event, while the general power of Congress to change its prior proposal may be argued, it is more than clear that in this instance Congress’ promulgation of the extension resolution was in violation of the constitutional requirement that Congress act by two-thirds of both Houses when exercising its article V powers.
In it’s answer to this question the court concluded:
Congress can set an arbitrary yet reasonable time period in order to establish a termination point for consideration and thus promote prompt action on the amendment by the states.
In other words, the court upheld that Congress can set a deadline for constitutional amendments.
So even if ERA activists are able to convince the US Archivist to proclaim that the ERA has been ratified, he’d be doing so in opposition to a federal court ruling that the deadline for ratification in the resolution was legal, and that deadline has passed. Likewise, if Congress votes via a 50% majority to abolish the deadline, they’d be doing so in defiance of that court ruling that a 2/3 majority would be required to do so.