Chris Evans abandons his Captain America costume for regular-guy duds in “Gifted,” an inspirational Hallmark Hall of Fame-style dramedy elevated to some extent not only by Evans’ amiability but by Marc Webb’s canny direction and a likable performance from young Mckenna Grace. But even those virtues can’t entirely compensate for the manipulative mawkishness at its center.

Grace plays Mary Adler, the seven-year old niece of Evans’ Frank, who ekes out a living repairing boats on the Florida shore. Mary’s single mother died—by her own hand—when the girl was just an infant, and she’s been raised—and home-schooled—by him. Now he puts her in public school, despite the warnings of their Earth Mother neighbor Roberta (Octavia Spencer) that doing so will draw attention to her remarkable ability in mathematics.

She’s right, of course, as the girl’s teacher Bonnie (Jenny Slate) recognizes her special talent and, together with the principal (Elizabeth Marvel), suggests that she be transferred to a school for the gifted. Frank adamantly refuses, insisting that what she needs is a normal life with regular kids for friends.

The reason for his concern is soon made clear when Frank’s mother Evelyn (Lindsay Duncan) appears on the scene. She’s a brusque, demanding New Englander who had pushed Frank’s sister to fulfill her brilliant potential as a mathematician by solving one of the world’s long-standing problems in the field (and winning a Nobel Prize in the process). She abandoned Mary to Frank after her daughter’s death, but now, having learned that Mary has inherited her mother’s ability, she shows up to take over the girl’s education—which, Frank knows, will involve the same unremitting pressure she placed on his sister, pressure that he believes led to her depression and death. A court case over custody ensues, in which Evelyn will play every card in her considerable arsenal, underhandedly if need be.

Everything in Tom Flynn’s script is by the numbers, though he does toss in a last-minute revelation that comes out of left field to resolve everything in a thoroughly implausible fashion. Before then, however, one has to contend with a subplot about a beloved pet—a one-eyed tabby, no less—that’s threatened with being put down, and an episode in which little Mary stands up to a bully who’s broken a smaller classmate’s diorama. We even get the formula-one sequence in which Frank and Bonnie agree about how wrong it would be to get intimate, and what immediately follows is…well, you know.

If the material is thin and crudely calculating, however, it’s at least made more palatable by mostly skillful execution. Webb has assembled a generally excellent cast, and though Spencer’s shtick as the all-knowing neighbor is more than a trifle thick, Evans deploys his considerable charm to keep the interaction between him and young Grace from becoming insufferably cloying. Grace matches him, avoiding the irksome precociousness that could easily have infected her performance by adding a touch of underlying stubbornness to the mix. Less successful is Duncan, whose turn doesn’t go much beyond a generalized haughtiness, with barely a hint of empathy beneath it. To compensate, the remainder of the supporting cast does its work quite well, with Slate exuding concern as Mary’s teacher (although the romantic subplot linking her and Frank is all too obvious) and Glenn Plummer especially winning as Frank’s lawyer.

“Gifted” is technically solid, though it certainly doesn’t exhibit the degree of big-money support that Webb’s “Amazing Spider-Man” movies had. Laura Fox’s production design and Abby O’Sullivan’s costumes do the job, and Stuart Dryburgh’s cinematography is appropriately unfussy. Rob Simonsen’s score, however, strains too intently to appeal to our emotions.

In the end, the problem with “Gifted” is that, unlike the little girl at its center, it turns out to be a quite ordinary exercise in heartwarming schmaltz.