George himself refuses to marry her because of her dark skin and it is from him that we learn of Miss Swartz Jewish lineage:
Other Jews appear in the novel when Becky and Rawdon Crawley attend an auction at the home of the bankrupt Sedleys. Becky comments to her husband,
"Look at them with their hooked beaks," Becky said, getting into the buggy, her picture under her arm, in great glee. "They're like vultures after a battle."
The derogatory comment was accompanied by the illustration above.
Thackeray himself was not anti-Semitic, though he had negative encounters with Jewish financiers in the 1830s. However, in his portrayal of Miss Swartz, he gives her no depth of character, though she has much affection for Amelia. She has basically no skills and the only reason George's sisters like her is her wealth. His description of those at the auction as vultures, unclean birds, is ironic when one considers who makes the comparison.
Israel at Vanity Fair: Jews and Judaism in the Writings of W.M. Thackeray by S.S. Prawer
Rhoda Swartz in Vanity Fair: A Doll without Admirers by C.J. Hegler