Yes, Granda of Spain copied it for them. The statue of Our Lady of Walsingham in Houston came from the Slipper Chapel as well. It was the copy used when the Statue of Our Lady of Walsingham blessed by the Holy Father had to be removed from the Slipper Chapel for repairs.
Look closely at the picture of the Houston shrine-church: the window on the right is of Our Lady, holding a miniature of the holy house, appearing to Richeldis. Son Geoffry is depicted as a grown man behind her, holding the St George banner indicating that he became a crusader.
The Houston Church has a lady chapel the exact dimensions of the original holy house. On the tabernacle door there is a bas-relief of the Holy Family in Joseph's carpenter shop. The walls of the holy house shrine is built to the height of the house of Loretto, and the steep roof is supported by rough oak hammer-beams. The tiny chapel is wonderfully "home-like".