
Souvenir of Velázquez probably dates from 1876. According to the Pennells, 'Greaves went with him to an Old Masters show at the Academy where they saw the Philip on horseback as Greaves called it - evidently the Olivarez or the Don Baltasar.' 1 This was probably the equestrian portrait of Don Gaspar de Guzmán (1587–1645), Count-Duke of Olivares (Metropolitan Museum, New York), which was owned in Whistler's time by the Duke of Elgin, and exhibited at the Winter Exhibition of the Royal Academy in 1876.

Souvenir of Velázquez, Private Collection
It is fully catalogued in MacDonald 1995 (cat. rais.) [more] (cat. no. 653).

Souvenir of Velázquez, Private Collection

Souvenir of Velázquez, Private Collection
A cavalier with sword, riding a rearing white horse.

Souvenir of Velázquez, Private Collection
This is a rough sketch of the equestrian portrait of Count Duke of Olivares (Metropolitan Museum, New York), which was owned in Whistler's time by the Duke of Elgin. Then attributed to Diego Rodriguez de Silva y Velázquez (1599-1660), it is now attributed to Juan-Battista Martinez del Mazo (1612-1667). Whistler could have drawn it from the original or a reproduction. He could have seen it in the Manchester Art Treasures Exhibition in 1857 (cat. no. 789), the Winter Exhibition at the Royal Academy in 1876 (cat. no. 116), and 1891 (cat. no. 113).
UPDATE:
There are big gaps in the known provenance.
'Nettie' or 'Netty' could have been born Agnes, Annette, Janet, Jeanette. Nettie Carpenter knew Whistler (who disapproved of her) and the impresario Otto Goldschmidt, and was said to have studied the violin under Pablo de Sarasate y Navascues (1844-1908). It is perfectly possible that Goldschmidt acquired the drawing directly from her.
Her biography is difficult to untangle. In 1891 Leo Lawrence Stern married Nettie Carpenter. In 1895 he successfully petitioned for divorce naming his wife as Nettie van den Berg Stern, and citing Harrison Brockbank. She married Brockbank in the following year. The 1901 UK census records her as 30 years old, born in New York, and married to James H. Brockbank, living with two Wagnerian children (Siegfried, Iseult) in Hammersmith, London. They separated in 1904. She continued to perform as a violinist under the title 'Madame Nettie Carpenter' until at least 1924.
Further details are given in MacDonald 1995 (cat. rais.) [more] (cat. no. 653).
1: Pennell 1921C [more], p. 120, quoting an interview between Joseph Pennell and Walter Greaves on 21 September 1906.