Yehia — whose father spoke on the condition that the family name not be published for fear of a backlash if it became known he had taken the boy to Israel for treatment — is the first Afghan treated by Save a Child’s Heart in its 20 years of operations. About half the charity’s 4,000 patients have been Palestinian; 200 others were children from Iraq and Syria, and the roster includes patients from Tanzania, Ethiopia and Moldova.

Israel boosters often highlight such programs as examples of the small nation’s outsized humanitarian efforts, including to hostile neighbors. Leora Robinson, a second-year medical student in Britain who is doing an internship at the charity, said that it provided an important counterpoint to portrayals of Israel as an occupier of Palestinian land, as she saw on campus during Israel Apartheid Week. “It opens eyes to the fact that this country doesn’t just have one side to it,” Ms. Robinson said.

But Tony Laurance, head of a group called Medical Aid for Palestinians, said that while providing children “world-class surgery” was “an unequivocal good,” it should not obscure the broader impact of Israeli policies on medical care for Palestinians. Gaza hospitals are perennially short of medicine, equipment and well-trained staff members, and many Gaza residents struggle to get exit permits for care outside the territory.

“What gets up my nose,” Mr. Laurance said, “is that it presents an image of Israel that betrays the reality.”