Not their

Hello...

In the below, the underlined part is difficult to understand.

Is this the abbreviated form of "They are not married in their understanding of marriage, no."?

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They're brown eggs. My house is very small . . . and white . . . one room. I see a man. I live with him. He has very curly hair and blue eyes." I asked if they are married. "Not their understanding of marriage, no."