The relevant section of the interview starts off with a casual remark by Irani while being asked about the Indian Institute of Technology-Madras' derecognition of a student organisation, the Ambedkar-Periyar Study Circle. The derecognition was perceived as being a response to the APSC's general anti-Modi positions. It came after the Minstry of Human Resource Development wrote a letter to IIT-M on May 15, forwarding complaints the ministry had received about the APSC.
In the interview, Irani attempted to assert that her ministry is not punitive when it comes to dissent (see from minute 21, in this video). "Ask anyone here who listened to an anti-Modi speech in IIAS Shimla [Indian Institute for Advanced Studies] by Ramchandra Guha, while I was minister?" Irani said. "Teesta Setalvad was also invited to this, while I was the minister."
Guha says he was alerted about the comment by someone who watched the interview, and immediately after seeing himself was appalled not just at what Irani said about him but how much in the statement was wrong. The speech was in Delhi, not Shimla; it was about Mahatma Gandhi and Varanasi, not an "anti-Modi speech"; and Teesta Setalvad was not a special invitee.
"Either she's misinformed, or she's telling a lie, or she's clearly ignorant about what's going on," Guha told Scroll.in. "There could also be another possibility, and this is personal speculation, but she might think that every time Ramchandra Guha opens his mouth, he's speaking against Modi."
My IIAS talk was at Delhi, not Shimla, and it was on Mahatma Gandhi and Banaras, not (as @smritiirani claims) an attack on the PM. 2/7
— Ramachandra Guha (@Ram_Guha) June 11, 2015
I have never made any speech anywhere attacking Mr Modi, though I have written articles critical of him, and of MMS, and of Rahul G 3/7
— Ramachandra Guha (@Ram_Guha) June 11, 2015
In sum @smritiirani 's claims that I attacked the PM under the auspices of an Institute under her control is a plain lie. 6/7
— Ramachandra Guha (@Ram_Guha) June 11, 2015
The lecture itself, the 19th Dr Sarvepalli Radhakrishnan Memorial Lecture given in memory of the former India President's decision to donate the Presidential estate in Shimla to establish the Indian Institute of Advanced Study, was, as Guha pointed out, focused on Mahatma Gandhi's relationship with Varanasi, a town that was also close to Radhakrishnan's heart.
A copy of the lecture shows Guha spent most of his time discussing Gandhi's various visits to Varanasi, including, almost ironically his first and most famous speech there in 1916, which criticised the British Raj as well as the opulence of the dignitaries present. That speech – an early anti-British address from Gandhi – caused much consternation at the time, with many guests walking out while it was still on, and Gandhi being forced to write letters placating some of them in the aftermath.
It is only towards the end of the speech that Guha turns his eyes to contemporary issues and only in one place does he actually mention Modi, in a reference to Varanasi.
"Long after Gandhi’s death, Banaras retains its central place in Hindu culture and society. Millions of pilgrims and tourists visit it every year. The place of the city in the popular imagination has recently been further magnified by the fact that our Prime Minister is the sitting Member of Parliament from Banaras. There is thus even more reason to revisit what the greatest modern Hindu had to say on his own visits to the city."
Guha's observation earlier in the speech that Varanasi is dirty, unequal and occasionally communal, would be hard to characterise as anti-Modi, never mind classifying the entire speech as being anti-Modi. Yet that's how Irani labelled the speech, going on to point out that it happened while she is minister, since IIAS is a government institute.
"I just felt that it's an insult to the memory of Radhakrishnan, a great scholar himself, to think that I would go on a diatribe instead of speaking about a scholarly topic," Guha said. "It does not behoove a cabinet minister to make such casual remarks. The government is receiving criticism, so they want to make it seem like we are so tolerant that we allow Ram Guha to attack them. Whether it is a deliberate falsehood or not only she knows. The HRD Minister should know what is happening."