For a trivially small set of mapping data, I like using VALUES to create a "virtual" staging table:

    UPDATE reward_members
    SET member_status = status_map.new_status
    FROM (VALUES ('gold',     'gold_group'),
                 ('bronze',   'bronze_group'),
                 ('platinum', 'platinum_group'),
                 ('silver',   'silver_group')
         ) AS status_map (old_status, new_status)
    WHERE member_status = status_map.old_status;