The paintings telegraph literal and figurative loss. In one, a soldier rests a gun on the sill of a broken window that overlooks a street gutted by explosions. “Mother’s Lament” captures six different video frames and features a woman in a double-layered veil and abaya, her face tight with anguish. In “Fallen” men snap pictures of the bloodied corpse of Mutassim el-Qaddafi, the son of the former Libyan strongman. The painting draws its images from 20 video stills stitched together from Mr. Foley’s raw video footage. Other paintings, of sky or desert, function as pauses between conflict photography.

“Bradley is not just giving us the most disturbing images — that’s certainly there — but also paying attention to what is the banality of war, its everydayness, little moments where you are just looking up, at a beautiful arrangement of light,” Dr. Mirzoeff said.

Since his graduate art student days at Yale, Mr. McCallum has spotlighted themes of justice and accountability in his work, including a stint as artist in residence for the New York Civil Liberties Union. His projects comprise collective portraits of women who lost children to gun violence, homeless teenagers and defendants in war-crimes trials at the International Criminal Court in The Hague.

Mr. McCallum received a $10,000 grant from the James W. Foley Legacy Foundation with an agreement to return some profits. The family established the foundation in 2014 to provide hostage advocacy services, education and journalist safety guides. During Mr. Foley’s captivity, his family said it experienced frustrating and fruitless attempts to work with the Obama administration and were instrumental in that administration establishing a new hostage recovery protocol involving families whose relatives were kidnapped abroad.

As the president of the Foley foundation, Mrs. Foley is practiced in being a public figure. Strangers send paintings and drawings of her son to the family’s New Hampshire home. The Foleys participated in Brian Oakes’s 2016 documentary, “Jim: The James Foley Story.” Sting wrote and recorded a song about Mr. Foley that was nominated for a 2017 Academy Award. Reporters phone the Foleys for reaction after a journalist is killed, most recently after the October murder of the Saudi Arabian journalist Jamal Khashoggi in Turkey. Earlier this year, when Mrs. Foley learned that a feature film was being made about a mother’s efforts to free her kidnapped son, a reporter in the Middle East, she asked whether it might harm conflict journalists.