under her breath

Tom Clancy's Net Force、昨日の続きの個所です。
"You're early," she shouted at him. "Go away and come back in fifteen minutes."
"It's OK," Roddy said. "I'll just wander around."
"Fine," Maj said, and added under her breath as she sat back down again, "Go ahead, freeze your butt off, I don't care."
"under her breath" はイデオムでしょう。辞書を見ます。
・Oxford English Dictionary: In a very quiet voice; almost inaudibly:: ‘he swore violently under his breath’
・Dictionary.com: below / under one's breath, in a low voice or whisper; sotto voce: He protested under his breath because he was afraid to speak up.
"sotto voce" はイタリア語ですが、日本語の「そっと言う」の連想で覚えやすいですね。