According to the website below, her paternal grandfather was born to unknown parents so it's difficult to see how you could establish any link with the Stewart kings of Scotland.
https://www.wikitree.com/wiki/Stewart-30994
Marlene Koenig has kindly sent me a link to the 1891 2nd edition of Americans of Royal Descent. It provides a descent for Anita from King James I of Scotland (that's a link). The descent is through multiple female lines so it is unconnected with the Stewart family name of her father.
Some of these published pedigrees from the 19th century are very "creative". I don't know how well proven this one is - but it certainly provides a good starting place for research.
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