Kim, who has been away from the public eye since the birth of her daughter North two months ago, posted a photo on Instagram of a tiny pair of pajamas along with a note from Couric.
"Dear Kim and Kanye, Congratulations on the birth of your baby girl! And may I humbly suggest you continue the K tradition," the note read.
The 32-year-old then went on to mock Couric's gift and note with a series of hashtags like 'hate fake media friends'.
Kim's sister Khloe tweeted her support shortly afterward, "God I love this new side of u!"
Curic, however, clarified that she did not mean to hurt the reality star with her comments.
"I've met Kim before and I think she's a really sweet person. I was responding to a reporter's question, and explaining how I'm intrigued by the public's fascination with her family. I didn't mean to hurt her feelings. The gift is genuine, and I'm happy for Kim and Kanye," Curic said in a statement.