Many people in the ancient world would not seek to "disturb, re-use, or rob" children's graves as they, "were less likely to contain the costly items tomb robbers sought." Many children's burial forms were small and, therefore, seemed worthless to thieves. So, Medea was not concerned with the sanctity of her children's graves because of the commonality of grave-robbing, but because she knew that the townspeople in Corinth would be displeased with her actions. But even though the Corinthians might have vengeance for their leader's murder, the chorus "treats her sympathetically" and would not desecrate Medea's children's bodies. It is more likely that Medea believed that, "someone who treacherously murders should offer his victim's extremities to the chthonic gods" and offered her children to Hera in that respect.
source: Holland, Lora L. “Last Act in Corinth: The Burial of Medea’s Children (E. Med. 1378-83).” The Classical Journal, vol. 103, no. 4, 2008, pp. 407–30. JSTOR, http://www.jstor.org/stable/30038003. Accessed 30 Jan. 2024.