In the clip shared by TMZ, the new parents were reportedly leaving a movie theater in Cleveland, Ohio, holding hands as they walked back to their car together.
In a photo shared exclusively by the outlet, the couple was also seen grabbing some snacks before their film started.
The new images of Kardashian and Thompson on an afternoon date come just one day after it was reported that the couple is trying to work things out in couples therapy.
"Tristan had no interest in going, but Khloe insisted on it," a source close the couple reportedly said, according to Radar Online.
"Her sister Kim advised her that it was a good idea, because their relationship was already going to be a challenge with a new baby around, let alone a cheating scandal hanging over their heads," the source continued.
"The sessions have been difficult," the source added, commenting on the couple's intense conversations with a professional mediator behind closed doors. "Their fights are monumental at the moment."
Eventually the source also revealed that Kardashian and Thompson "barely talk — except when it comes to the baby — but there have been some very frank discussions during the session."
"The relationship seems unlikely to survive," the source finally said. "Friends think there's no way Khloe wants to raise her daughter in such a toxic environment."
The new couples therapy report comes not long after reports that Thompson is allegedly in control of the relationship and has slapped her with a list of demands.
"Tristan continues to insist he's done nothing wrong, and blames Khloe's family for exaggerating his womanizing and trying to ruin his reputation," a separate source close to the couple reportedly told Radar Online, also adding that the Cleveland Cavaliers player has grown more controlling "in return for staying in Khloe's life in the long-term."
"He's willing to walk away, but Khloe's desperate to work this out, so Tristan's in the driving seat right now," the source also reportedly said. "He's agreed to stick around for now, but only if the family stops spreading stories, and he gets cut into Khloe's portion of profits for the show."
"He wants Khloe to let him see True any time he wants and insists she should fly out to meet him where he is. He can't just jump on a plane to L.A. when he's got a game coming up," the source continued. "What's really galling here is Tristan's 'you owe me' attitude. Khloe is actually considering some but not all of Tristan's demands."