It is thought that Carole clashed with Lindka over whether she was allowed to show the design to her friends in advance of the big day.
According to The Mail on Sunday, Carole requested that the unfinished dress - which was to have a matching tailored jacket - be delivered to her home, so that she could show it to her friends.
The designer responded by explaining that the request was 'unconventional' and that people usually come to visit her more secure studio . However, she agreed to the compromise that she would allow the outfit to leave her studio if she could personally accompany it to Mrs Middleton's home - to ensure that the designs were not damaged or leaked.
According to an inside source, Lindka was then taken aback when Carole branded her "unaccomodating" and then refused to wear the outfit, and has told friends that she's "completely bemused" by Mrs Middleton's actions.
"It is unheard of for a couturier to allow something out of their studio unfinished," said the fashion source. "Mrs Middleton wanted it to be delivered to her home pinned together, as if it were ready to wear."
A friend of Carole's has hit back, saying: "At one point she was intending to wear Lindka Cierach, but now she's found something she likes better, which is every woman's prerogative, and she has told Lindka this."
"Carole's entitled to wear whatever she likes. It is her daughter's wedding, after all. She paid her initial deposit and will be settling Lindka Cierach's bill in full."