Labour's Deputy Leader Angela Rayner called on the Conservatives to clarify the link between Jill Mortimer, a farmer and district councillor on Tory-run Hambleton council, and tax havens.
It was reported that before moving to Thirsk, some 30 miles from Hartlepool, Mrs Mortimer spent a decade living in London and overseas, including time in the Caribbean island.
In a letter to Conservative co-chairman Amanda Milling, Ms Rayner called on her to publish a full account of the candidate's time in the Cayman Islands.
She said: “I am sure I do not need to remind you that businesses that set up in places like the Cayman Islands tend to have a very specific motivation for doing so: namely, to avoid paying their fair share of taxes that contribute to running the public services we all rely on in this country. This kind of thinking is a million miles away from how most people live their lives.”
But in a reply posted last night, Mrs Milling said the party was aware that Jill Mortimer had spent a year living in the Cayman Islands "many years ago".
She said Mrs Mortimer moved there with her children due to the job of her ex-husband, "a highly experienced and respected regulator of financial services and a qualified barrister".
The reply said the ex-husband was "a leading authority on financial regulation and has worked and published widely on counter-fraud, anti-corruption, anti-terrorist financing and many other matters".
She continued: "As such, not least due to her ex-husband's role, Jill's family was scrupulous at all times in its financial affairs. We are happy to confirm that Jill Mortimer and her husband did not gain any tax advantage from living in the Cayman Islands, nor did she advise any others on this.
"We can also confirm that Jill Mortimer has no financial connection to the Cayman Islands. She has no financial interests such as bank accounts or any other assets and neither does her ex-husband.
"We are immensely proud that Jill Mortimer is our candidate for Hartlepool. Neither we, not Jill, will apologise for a woman supporting her family by following her now ex-husbands to various countries due to his important line of work in tackling corruption, money laundering and ensuring robust financial regulation.
"Your desperate attack has completely collapsed. Your misrepresentation of this period in Jill's life is factually wrong and entirely disingenuous. You surely do not oppose the work that Jill's family were doing during this period? And are you suggesting that a woman should be judged in any way on the work of her ex-husband?"
Some polls suggest Mrs Mortimer is ahead in the polls in Hartlepool, where the Conservatives are hoping to return an MP in the town for the first time since the 1960s.
Thelma Walker, who served as Labour MP for Colne Valley in West Yorkshire for two years and left the party last year, will also be bidding to win the seat for the newly-formed Northern Independence Party.
Labour’s candidate Dr Paul Williams is described by leader Sir Keir Starmer as "a tireless champion for the great town of Hartlepool".
The by-election will take place alongside the local elections on May 6 after Mike Hill resigned as MP for the north east constituency.
Hartlepool is a seat long held by Labour and the party fought off a strong Conservative and Brexit Party challenge at the 2019 general election, although their majority was reduced to just under 3,600, down from 7,650 in 2017.