The revised sentence with parentheses is Jeanette (winner of the spelling bee) always seemed to get an A's on her report card.
The main purpose of using parenthesis is to add extra information in a sentence without grammatically including the section that was added. In other words, you can use parentheses to add a comment, opinion, or remark that is not essential in the sentence.
In this context, to know how to place some parentheses you need to identify which piece of information is just a comment or remark.
Based on this, you can conclude the information that should be enclosed in parentheses is winner of the spelling bee because this is just extra information about Jeanette.
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