November 02, 2018 05:30 PM

Pete Davidson and Ariana Grande may have only dated for five months, but the fallout from their whirlwind relationship continues.

On Thursday, Davidson joked about the two recently calling off their engagement in a promo for the new episode of Saturday Night Live — which was quickly met with what appeared to be a rebuke from Grande. Responding with a sharply worded tweet seemingly directed her ex-fiancé’s way, the singer’s reaction prompted reports that Davidson was pulling a skit about their relationship from the weekend’s show.

However, a source close to the 24-year-old comedian tells PEOPLE that despite the backlash, Davidson may continue to reference their relationship.

“It’s completely untrue that Pete got a skit about Ariana pulled from this weekend’s show,” the source tells PEOPLE. “Anyone who knows SNL knows it’s still in the writing process even today, and no one knows what’s going on until dress rehearsal. Pete has always talked about his life on the show, and Ariana knows that. That’s where she met him in the first place.”

The insider adds, “Pete’s unfazed. It’s true they’re not in agreement about things after the breakup. A lot of people thought he was the wild card in the relationship, but that’s not true. Pete has and will always joke about his life, with or without her.”

Pete Davidson and Ariana Grande
Ariana Grande/Instagram

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In Thursday’s clip posted the sketch comedy show, Davidson introduces himself to musical guest Maggie Rogers and proposes to her in one fell swoop — a joke about his getting engaged after only a month of dating.

“Hey Maggie, I’m Pete. You wanna get married?” Davidson said as host Jonah Hill, 34, cringed standing between them. Rogers, 24, quickly declined and Davidson responded by saying he’s “0-3,” poking fun at his failed relationships.

Ariana Grande and Pete Davidson
Evan Agostini/Invision/AP/REX/Shutterstock

After the video was published, Grande, 25, wrote in a since-deleted tweet, “for somebody who claims to hate relevancy u sure love clinging to it huh.” She followed up with another that read, “thank u, next.”

Ariana Grande tweets about Pete Davidson
Ariana Grande/Twitter
Ariana Grande tweets about Pete Davidson
Ariana Grande/Twitter
Ariana Grande tweets about Pete Davidson
Ariana Grande/Twitter

Grande also retweeted the SNL trailer posted by a fan who wrote: “SNL is about to milk their breakup just like they did with the engagement.” Grande simply added “.”

RELATED: Ariana Grande Hides Another Pete Davidson Tattoo, Thanks Friends for Turning ‘Lemons Into Lemonade’

After seemingly coming for Davidson, Grande posted a few milder tweets on Friday afternoon — perhaps lyrics to a new song inspired by her heartbreak.

Prior to Thursday, things between Grande and Davidson appeared to be very civil.

The two called it quits in October after getting engaged in June.

“It was way too much too soon,” a Grande source told PEOPLE at the time. “It’s not shocking to anyone.”

Sources close to the couple told TMZ that the decision to split was a mutual choice, as both the pop star and Davidson felt the timing wasn’t right.

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