Although they had little interaction, Courtney admits that she had nothing "bad" to say about Leshawna (unlike with the other remaining campers--with the exception of Duncan), which was rare by her own admission.
Even though Courtney had no personal grudge against Leshawna, she orchestrated her elimination during the cufflink challenge in Cufflink, He Come to Town to hurt Harold as well as deprive him of a powerful ally. Leshawna became extremely angry at the CIT (as well as her allies Duncan and Heather) upon finding this.
Leshawna even came back to the island to see Harold in his crippled state after the Gummi Slug incident. She wasn't around to hear who had done it, but when Duncan and Courtney came to Playa De Losers, she chased them around to get back at what they did. Leshawna was full of spit-fire over the two throughout the rest of the season.
Even if Courtney turned over a new leaf, Leshawna wasn't so forgiving, and still held a grudge against her. Courtney was placed in the same team as Leshawna, as well as Tyler, Gwen (who both hated her too) and Hannah during the Train Race. They decided to have some payback at Courtney in the form of mild torture, such as tickling her feet for a long time or giving her a wedgie.
Later, during the Blimp Race challenge, Courtney and Leshawna were on the same team again, but this time Leshawna didn't show any animosity towards her, and Courtney didn't show any resentment for what happened during the train race. Courtney even went into Leshawna's defense when Colin was constantly insulting her (much to the sister's surprise), and they both teamed up to slap Colin unconscious during the slap fest challenge without even trading a word. It's assumed that their feud ended after this challenge.
- Their respective boyfriends have a feud of their own as well, which is still ongoing.