Identify a story about time travel with a prehistoric child and a modern-day carer who grows attached to him

Question

It's a short science fiction story about the invention of a time machine in the future. The tale revolves around scientists sending a child from the prehistoric era, who is cared for by a woman who grows attached to him. Later, a decision is made to return the child to the past. Because the woman has developed feelings for the child, she chooses to accompany him back without informing anyone.

Answer 1

"The Ugly Little Boy" a.k.a. "Lastborn", a novelette by Isaac Asimov, first published in Galaxy Science Fiction, September 1958, available at the Internet Archive. You may have read it in one of these compilations.

It was adapted to a 1977 TV movie, and in 1991 it was expanded by Asimov and Robert Silverberg into a novel which was published in the U.K. as Child of Time and in the U.S. as The Ugly Little Boy.

Wikipedia plot summary:

A Neanderthal child is brought to the present day as a result of time travel experiments by Stasis Inc, a research organization. He cannot be removed from his immediate area because of the vast energy loss and time paradoxes that would result, and is kept in the present by way of a Stasis module. In order to care for the boy the organization hires Edith Fellowes, a children's nurse.

Initially repelled by the boy's appearance, Edith soon begins to regard him as her own child, learning to love him and realizing that he is far more intelligent than she first imagined. She dubs him 'Timmie' and attempts to ensure that he has the best possible childhood despite his circumstance. She is enraged when the newspapers refer to him as an "ape-boy." Edith's love for Timmie brings her into conflict with her employer, for whom he is more of an experimental animal than a human being.

Eventually, her employer comes to the conclusion that his organization has exacted all the knowledge and publicity it can from Timmie and that the time has come to move on to the next project. This involves bringing a medieval peasant into the present, which necessitates the return of Timmie to his own time. Edith fights the decision, knowing the boy cannot survive if returned to his own time due to his acquisition of modern dependencies and speech. She attempts to smuggle the boy out of the facility, but when that plan fails she disrupts the integrity of the Stasis module and returns to the ancient past with Timmie.