Word's Bibliographies don't ordinarily include a border, so yours may have been customized somehow - presumably via paragraph borders. You can access the settings via Home>Paragraph>Border Button Dropdown. Depending on how things have been done, you may need to work through the Borders & Shading dialogue. Make sure you have the entire affected range selected before changing the borders.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]