The Methodology document for Nifty Indices (Page 133) explains how dividends are handled when calculating the index value -
Maintenance of NIFTY indices includes carrying out adjustments for corporate actions like stock splits, stock dividends, share changes and scheme of arrangements. Some corporate actions, such as bonus, stock dividends*, stock splits and reverse stock splits require simple changes in the equity shares outstanding and the stock prices of the companies in the index.
Other corporate actions such as change in equity, rights issue of shares, special dividend, change in investible weight factor (IWF) / free float results into change in the market value of an index overall and require a divisor adjustment to prevent the value of the index from changing
* - The word stock dividends isn’t mentioned in the current document but was mentioned in the previous index methodology documents (page 7)
Varsity mentions that ETFs follow the TRI version of the index -
Note: Always compare the ETF price with the total returns index (TRI) and not the price returns the index (PRI). The TRI includes dividends. All the index data you see on Kite is PRI. Since ETFs track TRI indices, they re-invest the dividends which reflects in the NAV of the ETF.
In case you are interested, the Methodology document for Nifty Indices (Page 136) talks about how TRI calculation is done -
Also check this blog post by @deepakshenoy - The Total Return Index: Nifty Including Dividends