Alito authored that decision, called Dobbs v. Jackson Women's Health Organization, and the Hobby Lobby one.
Schenck said he was motivated to come forward out of fear Supreme Court staff could unfairly take the blame for this year's leak.
Chief Justice John Roberts directed the Supreme Court's marshal to investigate the leak in the Dobbs case, calling it a "betrayal."
Democratic lawmakers said Schenck's account underscored the need for legislation requiring the U.S. Supreme Court, which now has a 6-3 conservative majority, to adopt a code of ethics, which unlike lower-level federal courts the high court lacks.
"I believe we pushed the boundaries of Christian ethics and compromised the high court's promise to administer equal justice," Schenck said.