The option contract or option chain LTP on Kite may differ from NSE if the option is illiquid. For illiquid contracts, NSE provides a theoretical settlement price if there are no trades in the last 30 minutes of the trading session. Kite updates the Settlement Price in place of LTP the next day when Zerodha receives a report from NSE called BHAVCOPY.
You can learn more about BHAVCOPY by visiting tradingqna.com/t/what-is-bhav-copy-published-by-exchanges-and-how-is-it-useful-also-why-is-it-called-bhav-copy.
In the below images, Kite displays the settlement price. However, the option chain on NSE shows the LTP.
On Kite
On NSE