The customary invocation of God is not what makes it legal. This has come up even in early times because Quakers would not swear oaths.
Then she's a perjurer, and the committee knows it.
Let's see if any of the spineless jellyfish known as Republicans even thinkof bringing it up. If they hd any principles left, they'd demand that Fitznifong or some other prosecutor brign charges against her. But the odds against any of them doing anything but apologizing are about 300 million to one.