Jean traveled home by way of London, as the last postcard mentioned. The Haywards took passage from Liverpool on August 1, 1908 on the S.S.
Cedric Cymric. The Cyrmic was a ship in the White Star Line. Here is the ship's manifest showing the Haywards arriving in Boston.
They were United States citizens, so the information recorded about them and their destination was not as detailed as it was for an immigrant.
Here is a blog post with recommendations for young Utah women traveling by sea, which incidentally described much of what Jean must have experienced at the time.