GROZNY, Russia — Every day, Belant Zulgayeva gets a knot in her throat watching her grandchildren play their violent games, what she calls their “little war.” They talk very little, but they run around, hide and, occasionally, slam one another to the ground with a disturbing ferocity.

Ms. Zulgayeva is on the front line of a different kind of struggle: an effort by the Russian government to bring home and care for Russian children like her three grandchildren, who were raised by Islamist militants in the Islamic State, also known as ISIS or ISIL.

As the American-led coalition and Syrian government forces captured cities that had been held by the Islamic State, they found among the ruins a grim human wreckage of the organization’s once successful recruitment drive: hundreds and perhaps thousands of children born to or brought with the men and women who had flocked to Syria in support of the Islamic State.