The case
The mall food court original. The sign has always said Chick-fil-A, a pun on chicken fillet with an A for grade-A. The K is where the memory drops it.
Written out, the name looks like French, so a lot of people spell it as if it were and lose the K. The chain has been gently correcting customers for decades.
Why our brains do this
A name that looks foreign gets spelled by foreign rules, and the English "chick" loses its K.
Sources: Wikipedia — Chick-fil-A · Wikipedia — False memory: the Mandela effect