Kayley Asher, 25, was attacked by Allitt while being treated at Grantham Hospital as a baby.
She received £11,500 compensation but social security officials say she failed to notify them of this and must return benefits she has received.
Her parents, Alan and Sharon, say they have "no intention" of giving the money back and are prepared to go to prison.
Miss Asher, from Grantham, received an Employment and Support Allowance (ESA) for five years because she is unable to work and also a £120-a-week disability allowance.
Her parents said they used that money for her day-to-day care and were given the £11,500 in compensation when she turned 18.
However, the Department for Work and Pensions (DWP) says she failed to declare the payout when applying for the ESA, which is a means-tested benefit.
"We have never hidden the fact that Kayley had this money," said Mr Asher.
"We always believed that compensation was for her future. It was awarded because she needs special care."
Allitt was given 13 life sentences in 1993 for murdering four children and attacking nine others while working as a nurse at Grantham Hospital.
It is believed she injected 13-month-old Miss Asher with air under her armpit, causing her to have two heart attacks.
"The murderer had a go at her once and now the DWP are causing Kayley pain. It is totally wrong," said Mr Asher.
"We have no idea what the future holds for us.
"With a sum of money her future is secured if anything happens to her mum and I."
He said they intended to appeal against the DWP's decision and would risk going to jail.
A spokeswoman for the DWP said: "It is essential that claimants declare their income and savings accurately. This is to ensure that support is targeted at the people that need it most."
She said other non-means tested benefits were available to Miss Asher.

The artwork, by US sculptor Charles Ray, will be replaced by a lamp-post at the tip of the Punta della Dogana.
The decision has angered some art lovers who argue that it shows a failure to embrace challenging, contemporary work.
But city officials say the sculpture was always intended to be temporary.
Boy with Frog, which is gleaming white and 8ft (2.5m) tall, has occupied the tip of a triangular piece of land that separates the Grand and the Giudecca canals for almost four years.
It shows a boy holding up a frog by one leg and gazing at it.
The sculptor had earlier expressed hope that his work would become a permanent "citizen of Venice".
"I never saw it as temporary," Mr Ray told the New York Times.
But some residents reportedly missed a 19th Century lamp-post, long a romantic meeting spot, which stood at the spot before.
Workers began to remove the sculpture overnight on Tuesday ready to clear the space early on Wednesday, Corriere del Veneto newspaper reported.
In its place will be a reproduction of the original lamp-post.
The old-fashioned landmark was thought to be more in keeping with the surrounding architecture, BBC Rome correspondent Alan Johnston reports.
Some animal-lovers also argued that the image of a boy holding the frog upside down was cruel, our correspondent adds.
But a piece in La Stampa newspaper criticised Venice's council, saying "administrative cowardice" had won out over real culture.
Defending its decision, the council said the sculpture had been considered temporary and Venice had a fine record of welcoming and exhibiting modern art.

The 25-year-old scored one goal in 58 games in two seasons for the U's, having moved from Rotherham in 2015.
Newton began his career at Newcastle United but never made a first-team appearance for them.
His most successful stint came on loan to St Mirren, where he won the Scottish League Cup in 2013.
Find all the latest football transfers on our dedicated page.
A woman left brain damaged by killer nurse Beverley Allitt has been ordered to pay back £23,000 in benefits.
[NEXT_CONCEPT]
Work has begun to take away a controversial statue depicting a naked boy with a frog in a part of ancient Venice, Italian media report.
[NEXT_CONCEPT]
Hartlepool United have signed midfielder Conor Newton on an undisclosed contract following his release by Cambridge United.