Caroline Anthony was there for two years, 1817 and 1818, and the name James Gordon may be associated with hers in the ledger.
Henrietta Anthony was there for four years, 1811-1814, and an H. Anthony is associated with her account in the school ledger.
That doesn't seem like much to go on--no hometowns, no definite parent names, no reason to believe they're even related to each other. But there was pair of sisters, Henrietta and Caroline Anthony, who turn up in Southside Virginia Families Vol. 1 as the daughters of John Anthony (d. 1812) and Elizabeth Hill. John Anthony was apparently from Philadelphia, a cousin of the portrait painter Gilbert Stuart. Elizabeth Hill was the daughter of Col. Whitmel Hill and Winifred Blount--which connects these girls to the Hills, the Alstons, the Blounts, the Pollocks, the Nashes, the Camerons, the Norfleets, and many other families in the neighborhood of the Mordecai school. There's mention in one family history that Caroline was raised in part by her older sister--which would neatly explain the "H. Anthony" next to her name in the ledger.
So, retelling their story in light of what we can find in online genealogies...
Henrietta Maria Anthony left her home in
Henrietta married a Cyrus Dillard of Surry County, Virginia, in 1817, and had at least two children, Joseph and Henrietta (b. 1829). Caroline married a William Henry Pegram (1803-1852) in October 1824, and had four children between 1825 and 1842. Her daughter Ann Pegram died as an infant; Caroline Pegram was widowed at age 46, when her youngest child was ten. (That boy, William Anthony Pegram, would die in the Civil War ten years later.)