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Should it say:
Love, The Griffiths'
Love, The Griffith's
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Neither. You do not want the possessive, you want the plural. If your surname is 'Griffith' it should be 'The Griffiths'; if your surname is 'Griffiths', it should be 'The Griffithses' (I know the latter looks awkward, but it is correct-- apostrophes are best saved only for possessives).