Lea said, “It’s disappointing, because I was under the assumption that the mask was approved for use because it was issued by the U.S.O.C.”

Darryl Seibel, a spokesman for the U.S.O.C., said he was not aware of any reprimand. But he said the Olympians should feel free to wear their masks around the athletes’ village. Other United States teams, including the swimming squad, have been discussing when and where to use the masks.

“We’ve said all along that it is the athletes’ choice whether to wear one if they feel it’s necessary,” Seibel said. “I’m no scientific expert, but walking through an airport doesn’t seem like the place where it would be necessary to wear them.”

Image A cyclist from the U.S. team arrives in Beijing wearing a mask. The United States Olympic Committee's lead exercise physiologist advised U.S. Olympians to wear the masks on the plane and as soon as they stepped foot in the city. Credit... Issei Kato /Reuters

Earlier this year, Jacques Rogge, the president of the International Olympic Committee, said he was confident the air would be clean because Chinese officials “are not going to let down the world.”

Officials in Beijing, one of the world’s most polluted cities, promised the sky would be clean for the Olympics, but as the Games have drawn closer, officials have been forced to take extraordinary measures. Factories in the city and in the surrounding provinces were shut down or moved. Major construction was halted. Cars were taken off the road on alternate days.

But the sky remained thick gray this week, prompting some athletes to take precautions.

Months ago, Wilber, who did not respond to e-mail messages late Tuesday night, said he feared this would happen. He knew that wearing the masks ran the risk of offending the host country and creating political tension. In turn, he advocated that many teams train away from Beijing until just before their events.