"I asked Mr Burnes how could this be done so quickly, he verbally advised me, 'Hockey owes me'," Mr Carstensen wrote in the letter to a Senate committee, released on Thursday.
Mr Shorten said allegations a powerful Liberal donor had boasted about his links to Mr Hockey were not a good look.
"Personally I think Joe Hockey is a very nice person and he's done some good work in the US, but what was he thinking?" the opposition leader told reporters in Canberra on Friday.
"I don't think we've heard adequate explanation yet."
Senior opposition frontbencher Anthony Albanese said Mr Hockey was directly involved in organising meetings between the government a company he had a financial interest in.
"Helloworld, hello conflict of interest," he told the Nine Network.
"They are shares that increased, by the way, in value at around 170 per cent once these government contracts started flowing through."
Finance Minister Mathias Cormann said the 2017 contract awarded to Helloworld was made through the department's tender process which is independent of Mr Hockey.
"Bill Shorten knows that Joe Hockey is doing an outstanding job in our national interest in the US," the finance minister told Sky News.
"There is nothing in the smear that Labor has been throwing around this week that detracts from that."
Senator Cormann said Helloworld had made an administrative error in not charging him for a family holiday booked through Mr Burnes, as revealed this week.
The minister has now paid $2780 for flights to Singapore in January 2018, after it was revealed he was mistakenly not charged for them.
"When it was brought to my attention that a payment I was certain had been made had not been processed I was absolutely mortified," he said.
Mr Burnes emphatically denies the allegations that he called in a favour to help set up the meeting.
"Joe Hockey and I have been close friends for 20 years and it would be ridiculous to suggest I would say or imply he owes me anything," the Liberal Party treasurer told The Sydney Morning Herald.