Why Khloé Kardashian Didn't Care About Getting a Push Present from Tristan Thompson

Khloé Kardashian‘s baby girl, True, is the greatest gift she’s ever received.

In April, the Good American founder welcomed her first child with boyfriend Tristan Thompson. But unlike her younger sister Kylie Jenner, who got a Ferrari LaFerrari as her push present for daughter Stormi’s birth in February, a tangible item from Thompson wasn’t necessary for Kardashian, 34, to celebrate her first pregnancy.

“A push present never seemed important to Khloé. After she gave birth, she was just so happy that her baby girl was here,” a source tells PEOPLE.

Ahead of True’s birth, Kardashian was focused on other things — including her fractured relationship with Thompson, who was videotaped getting close to an unidentified woman in a New York City lounge, days before their daughter’s April 12 birth.

“Tristan was in the dog house and she barely spoke to him for days after the birth,” the source shares. “Kris [Jenner] helped her get settled at home with True while Tristan would visit the house.”

The source adds that, “Khloé had many other things to focus on. One of them was definitely not getting a push present from someone who had just cheated on her.”

Since Thompson’s cheating scandal broke, the couple has been focused on rebuilding their life together, including spending the summer in Los Angeles with her family.

Though Kardashian is committed to the relationship, she’s “still dealing” with his alleged infidelity — and her initial plan to relocate to Cleveland as Thompson’s basketball season begins has been put on hold.

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A source previously told PEOPLE, “It’s of course difficult to trust someone 100 percent who cheated days before he was about to become a dad.”

The source shared, “Khloé still struggles with this sometimes. She wants to move back to Cleveland, but she isn’t sure what date she is [going]. The move is postponed for now. She seems very upset about leaving her family. She had the best summer in L.A.”

Still, it appears as though Thompson wants to commit to Kardashian — and it could include an eventual ring on that finger. In a scene from Sunday night’s episode of Keeping Up with the Kardashians, Thompson FaceTimed Kris Jenner to discuss a push present for a then-pregnant Kardashian.

“I remember Koko saying she wanted something where she could pass it down, generation after generation,” he said.

“You know, Corey [Gamble] bought me for Christmas a couple of years ago this really beautiful little diamond ring that you could put on any finger,” suggested Jenner, 62, before gushing: “You know, until you get that really huge diamond that’s going to go on on her ring finger!”

“Of course,” replied Thompson. “Eventually!”

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While the new mom has mostly avoided publicly discussing the scandal, she addressed it on social media last month while responding to speculation that she and Thompson were talking about getting married. In a comment, she denied the rumor and responded to an Instagram user who accused her of “acting like Tristan didn’t cheat.”

“I’m not acting as if Tristan didn’t cheat,” she wrote. “I’m saying the story about marriage and anyone insinuating they know what we speak about privately is ‘crap.’ “

At the time, an insider told PEOPLE that while Kardashian and Thompson were “doing great,” there was “no mention of an engagement yet.”

“They are still working through stuff, but it very much seems they will stay together,” said the insider.