Rashi says when defining ארמית [Sanhedrin 82a] - "בת עובד כוכבים".
The issue is not her father but HER status. Rashi should say "עובדת כוכבים".
In the same vein, the Rambam ['איסורי ביאה י"ב ד] says that there is no דין of קנאים פוגעין בו for a בת גר תושב. A Jew from the USA visited Rav Dovid Soloveitchik on Chol Hamoed Pesach תשס"ב and asked him why it says בת" גר תושב"? The issue is not the status of her father as a גר תושב but what SHE is?!
[Related by Rav Moshe Mordechai Shulzinger ztz"l]
