Birkeland said the women did not touch her, but she was emotionally shaken.
"I came out crying," she said.
Birkeland said she didn't report the comments to police.
The challenge to Trump's ascension brought a heated response from Trump supporters and competing chants and yelling between the two sides.
But Paul Manafort, Trump's top campaign strategist, brushed off Birkeland's story on Tuesday, according to the Weekly Standard.
"I think I have a pretty good sense of what's going on in this convention, but I haven't gone in to the bathrooms yet," Manafort told reporters.
Utah Delegation Chairman Phil Wright offered the motion to try to overturn the rules.
He said later — when informed about what Birkeland said — that political disagreements should never escalate like that.
"Obviously, that's a horrible thing for anyone to say," Wright said. "That's a legal issue when someone is threatened."
Police officers have been posted at hotels with state delegations, including Utah's group, which is staying in Akron.
Bruce Hough, the Utah GOP's national committeeman and a sergeant-at-arms and officer of the convention, spoke with Birkeland and said that while he understands nothing physical occurred, "verbal abuse is not acceptable."
He said that if Birkeland can identify the women who threatened her, he would investigate.
Another Utah delegate, Stefani Stone Williams, received an intimidating email from Carl Paladino, the co-chairman of Trump's New York campaign, saying she should be "hung for treason" for being an activist working to give delegates the ability under the rules to vote for a candidate other than Trump.