Kishor, who earlier worked with the BJP but turned into its strident critic of late, reacted with indignation, saying he would retire from public life if the allegations were proven true.
He also asserted that those levelling the allegation against him should apologise.
In a statement, state BJP spokesperson Nikhil Anand asked by whose permission did Kishor, who is neither a government official nor a crew member of any air carrier nor a medical personnel, travel to Kolkata.
"Why must this travel not be considered illegal in view of the lockdown?" he asked.
"We demand that the documents which have facilitated his travel, secretly in a cargo plane dodging the lockdown, be made public. Else we would put pressure on the Airport Authority of India and the Civil Aviation Ministry to order an inquiry into the episode," Anand added.
He also alleged that Banerjee, who also heads the ruling TMC in West Bengal, has been a failure in tackling the coronavirus crisis and incapable of even optimally utilising the funds and resources provided by the Centre.
Anand said she had summoned Kishor for an image makeover.
"Her reposing trust in a political tout is an insult to corona warriors of her state who are doing their best despite her questionable leadership," remarked the BJP leader, whose party has been aggressively trying to make inroads into West Bengal ever since its spectacular performance there in the Lok Sabha polls last year.
Kishor appeared peeved at the allegations and told "if he (the BJP spokesman) is speaking the truth, he should furnish details like which flight I boarded and the time when it took off and landed.
"If he does so, I will retire from public life. If not, people like him should apologize."
Notably, besides the BJP spokesman, Ajay Alok, a fiery leader of the JD(U), which had expelled Kishor a few months ago, also shared a news item about the poll strategists alleged travel to Kolkata with a snide remark aimed at the West Bengal chief minister.
"During the pandemic people are seeking masks, sanitizers, ventilators and other equipment alongside doctors and nurses. Didi (the Bengali word for elder sister which Banerjees supporters and detractors use to address her) ordered such a heavy duty cargo item," Alok exclaimed in his tweet.
Kishor also pointed out that the flight operations are controlled by the Directorate General of Civil Aviation and the concerned Union ministry. With the BJP in power at the Centre, it should not be difficult for those levelling allegations to come up with proof in support of their claim.
Kishor, who first shot to fame in 2014 Lok Sabha elections when he handled the poll campaign of Narendra Modi, joined the JD(U) headed by Bihar Chief Minister Nitish Kumar in 2018 and was catapulted to the party's national vice president's post within weeks of joining it.
He was sacked when he launched a personal attack on Kumar, disputing the latter's contention that he was inducted into the JD(U) upon the recommendation of Amit Shah, who was then the BJP president.
Kishor has been hired by the TMC to give it a boost in the 2021 Bengal polls. NAC SNS RAXRAX