During Sunday night's episode, Pete and Kate cleared the air, as the comment was said to have angered Megan and Pete, who is now dating her.
The joke stemmed from a TOWIE quiz two weeks ago where quizmaster Arg had asked: "What's the name of Pete's dog who got introduced to Lockie?" Kate had said from across the table, "Megan McKenna".
On Sunday's episode, after bumping into each other in the supermarket, Kate said to Pete: "I've heard you've got the hump with me."
Pete admitted he did have the "hump" with Kate, saying: "The way it came across because she weren't there, was like it was bitchy."
Kate, who insisted it was a joke, said if one of the boys had said, it would have been "brushed under the table".
Pete continued: "That's the difference because we're all pals and where you and Megan ain't that close, but I thought it was a dig at her. I don't really want to get involved, she can fight her own battles. Maybe it's just a bad joke that's been taken the wrong way."
Defending herself, Kate said: "You're my friend though so it was more banter to you... It ain't a battle, it was just a joke. I thought it was quite funny."
Pete replied: "I know you're not a nasty person and Dan wouldn't be with someone that's like that anyway. Now she's sweet, she's fine."
Later, deciding to miss the Greek party and go out to dinner instead, Pete told Megan that he had earlier bumped into Kate.
Megan said: "I think a few years ago when the whole Kate thing would have happened I would have just wanted to go to the party just to confront her. But now it's like whatever. If she has an issue then she has an issue but I've got better things to worry about than what Kate Wright's got to say about me."
Pete told her: "She said it was a joke and I do believe her."
Megan replied: "Okay, I'll give her a chance."
TOWIE airs every Wednesday and Sunday at 10pm on ITVBe.
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