"It is awkward, especially for maybe Tristan, who isn't used to this," she told host Ellen DeGeneres.
Kardashian's sister Khloe Kardashian gave birth to her first child, daughter True, in April following reports Thompson cheated during her pregnancy. Recent episodes of Keeping Up have shown the drama unfold.
"Unfortunately, that was what's going on in our lives," Kardashian said. "So six months later, when it replays and they've gotten through what they needed to get through and it's rehashed in front of everyone and everyone's giving their opinions all over again and we're live-tweeting and everyone's chiming in."
"That is hard for Khloe, and I'm sure for Tristan, but it's our reality," she added. "We've learned to kind of use it as a therapy just to kind of get it out one last time with everyone else."
Sunday's episode showed Thompson in the delivery room at True's birth. Khloe took to Twitter after the episode to explain why she wanted Thompson there days after the scandal broke.
"I made it very clear that I was still disgusted by his actions but I wasn't going to let ANYTHING ruin this moment I've been waiting for my ENTIRE life," the star wrote.
"Regardless or what Tristan did to me, I was never going to take that moment away from True or Tristan," she said. "She should not be punished for his actions. He is her father and they both deserve to love one another as deeply as They possibly can."
Khloe and Thompson, an NBA star who plays for the Cleveland Cavaliers, have reconciled since the scandal. Thompson shared a photo with Kardashian and True in October while celebrating Halloween as a family.