The painting, by Dean Proudfoot, depicts Iti holding a gun and a skull in front of an Australian flag on the ground, with its misspelt title.
Above the now crossed-out spelling, he paints "Tāme" in white.
Art collector, philanthropist and hotelier Chris Parkin who owns the QT Hotel and the artwork within it told Stuff he saw the correction as "vandalism".
"I expect the police to prosecute him. They certainly would me if I went to Te Papa and vandalised an artwork."
The Herald has contacted Parkin for further comment.
However, the artist who created the work says he believes it has been elevated by Iti's correction.
Proudfoot told the Herald he apologises "unreservedly" to Tāme for the misspelling.
"There was no offence intended – it was a clear lack of research on my behalf."
He said the series in which the work is part of is about celebrating Aotearoa's "unique characters".
"Tāme is the epitome of what makes our country special."
He added that in his view, the correction has given the work a new life with a far more "powerful" meaning.
"It has been elevated. I thank him for that and for what I've learnt as well."
When contacted by the Herald for comment, an NZ Police spokesperson said "anyone who makes a complaint to police has the right to privacy".