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8:45 AM PT -- Sources close to the couple tell us Pete won't reference the breakup when 'SNL' airs, and the reason is ... the exes have an agreement to stay silent.

We're told the split was mutual, and Ariana and Pete verbally agreed neither would talk about it publicly -- but she was already feeling betrayed because Pete joked about it during a standup routine last week at a charity event. We're told it got worse when Ariana saw the promo.

Our sources say Pete got word Ariana was upset, and decided he didn't want to go through with the skit he'd written for this week's 'SNL' -- they had an agreement, after all. He discussed it with executive producer, Lorne Michaels ... and he signed off on pumping the brakes.

As for the promo airing? We're told it was already in the works, and it was too late to pull it.

The breakup ain't funny to Ariana Grande anymore -- she came for Pete Davidson on social media Thursday night after he joked about their breakup ... and it's clear, this ain't no conscious uncoupling.

Davidson cracked a joke about the fact he's single during a promo for this weekend's 'SNL' -- asking musical guest Maggie Rogers if she wanted to get married.

Our sources connected to 'SNL' say Pete had been in good spirits while prepping for the show -- and was open to making jokes about jumping into relationships too soon.

So, that's what happened during the promo ... but Ariana Grande wasn't laughing -- she tweeted a shot at her ex.

"For somebody who claims to hate relevancy u sure love clinging to it huh. thank u. next."

She later deleted the tweet.

Pete previously joked about their engagement when 'SNL' came back from summer recess -- but that was when he and Grande were still together.

The jokes were self-deprecating about how Grande is the breadwinner in the relationship -- and he was just lucky to be there.

But, they broke up last month, and clearly they ain't on good terms.

No word if Davidson planned on addressing the split on this week's show -- but if he was, ya gotta believe he's rethinking the plan now.