Call Option Expiry (ITM) - Excer

I bought 28000 CE at INR 7 and at 3:30 PM the Nifty Bank Index was at 28,064.5.

The premium was only at INR 14, hence trading at a large discount, even after factoring in the 0.125% fees on entire amount charged by SEBI (Which would have added up to INR 7,000 out of a total profit of INR 13,500 approx).

However, i did not want to take a chance and sold it at 3:30 PM for INR 13.6 when the NIfty Bank index was at 28,064.5 and still shows on the chart (ChartIQ in Zerodha)

At 3:31 PM it changed the Bank Nifty close to 28.013.45.

Can someone explain how the Bank Nifty index dropped from 28,064.5 at 3:30 PM to 28,013.45 at 3:31 PM? I use Zerodha and on the chart it is still showing 28,064.5.

The closing price is the weighted average of price in the last half hour of trade. And options are settled on the closing price instead of the Last Trading Price of the day. Options traders usually factor in this difference.
In your situation 28064 was last trade price at 3:30 but 28013 was Close price( weighted avg of all prices between 3 and 3:30)