"It's really impossible for me to pay," she said.
In a statement to the Herald, 2degrees said it looked at Kaur's data usage which tallied to 200MB on her device during her time in India.
A spokesman for the company said: "Smartphones are capable of accessing online services without customer intervention and in this case it would seem the phone did connect with Apple, and to Skype and a number of other services.
"We advise all travellers set a spend control before they travel so as to ensure they don't spend more than they realise, and to check pricing at the destination they're visiting. Customers who don't want to use data while roaming must change the settings in their device before arriving in country."
Kaur said the situation was upsetting, and that she was confused as she had used her father's wifi and hotspotted her mother-in-law's internet - the same way she had on a previous trip to India in September 2017, for which she had received a bill of about $100.
"When you see a bill like that - $2,600 - it makes your eyes open wide," Singh said. "That's more than what she paid for her tickets."
Kaur contacted 2degrees on Wednesday and tried to get the data charges waivered but was told she would have to pay $2000.
"[The person I spoke with] had a word with his colleagues and he said I would have to pay $2021 by 6th March, no matter what," Kaur said.
A 2degrees spokesman told the Herald the company could not comment any further as it was still in discussion with Kaur.
Last month another 2degrees customer contacted the Herald fuming over a $500 global roaming bill for data he also said he did not use.
Tauranga man Brendon Johnston, holidaying in South America, said he had been using hotel wifi so was horrified when he returned home to received a $508 charge for 50.81MB of data usage.
2degrees said he did use the data but waivered the bill as a goodwill gesture.