Under the original measure, which generated controversy in the fall, all 500 school districts statewide would have been required to display the words prominently in some fashion in every school.
Andy Hoover, legislative director of the American Civil Liberties Union, which objected to the original bill, said the House did the right thing by removing the mandate language so schools would not be forced by law to post the phrase.
But, he said, the legislation does not guarantee there will be no challenges.
"A blessing from the state House doesn't make it constitutional," Hoover said. "Schools that post it will certainly face First Amendment challenges."
Rep. Michael H. O'Brien, a Philadelphia Democrat, called the vote "an act of silliness."
The vote came on legislators' first day back in session and at the start of a crucial month.
O'Brien said the House was focusing too much time on moving religion-related bills when it ought to be concentrating on the state budget, which must be approved by the end of the month.
"This is a slow and steady step toward theocracy," he said. "We should deal with the budget, a fair and equitable Godlike budget."
The national motto has Pennsylvania roots.
Former Pennsylvania Gov. James Pollock put the words "In God We Trust" on coins in 1864 as director of the U.S. Mint.
The phrase was adopted as the national motto in 1956 under an act signed by President Dwight D. Eisenhower.
The amended version of the state House bill also would give school districts permission to post the Bill of Rights in schools.