Ron and Penny Jones are claiming Surrey County Council have been negligent for placing Ahmed Hassan with them without informing them that in a January 2016 immigration review the teenager had admitted he had been trained to kill by the Islamic State terrorist group.
The couple say they only found out this information at Hassan's trial and had instead been told by the council that Hassan had been captured by Islamic State but had escaped.
Hassan was handed a life sentence aged 18 last year after being found guilty of planting a bomb in September 2017 on a tube train at Parsons Green, which partially exploded injuring 51 people.
The bomb had been made by Hassan, who was an asylum seeker from Iraq, at the Joneses' kitchen table, while his foster parents were away on holiday.
Since the trial, Surrey County Council has stopped the Joneses from fostering, and the couple also claim that their right to a family life, under the Human Rights Act, has been breached.
The couple have fostered 269 children over a 47-year period for Surrey County Council and were awarded MBEs in 2010.
The Joneses' legal action is being crowd funded via Crowd Justice and has so far reached £3,800 of their initial £3,000 target. They hope to raise £8,000 to cover the insurance premium of their case.
"On the 15 Sept 2017, Ahmed Hassan left a bomb on the tube at Parsons Green station. A bomb he had built in our house," said a statement from the couple.
"However, Surrey County Council did not tell us that they knew he was 'trained to kill by ISIS'.
"We believe the council was negligent in not telling us the full story about Hassan's ISIS past and that they have breached our right to family life under the Human Rights Act."
The couple are also taking the legal action to ensure that other foster carers are made aware of serious concerns about young people being placed with them.
"We feel like we have given up our lives to Surrey to foster kids and they have turned around and betrayed us. We have been scapegoated and hung out to dry for somebody else's mistakes," adds the couple's statement.
"We want to make sure that no other foster carers are ever treated like we have been. This is about more than just our case, foster carer workers are misinformed every day by their local authorities.
"We believe in the transformative power of foster care. But to be done right it must be supportive to those of us who open our homes to children."
Last year, a review into police and Surrey County Council's involvement in Hassan's case revealed a raft of failings.
A letter from the home affairs select committee following the review said: "There was an apparent lack of formal, documented plan to manage and mitigate Ahmed Hassan's vulnerabilities and associated risks."
The committee also recommended all social care staff and managers should receive training around radicalisation.
A Surrey County Council spokesman said: "We are defending this claim. However, we acknowledge this has been a very difficult time for Mr and Mrs Jones and their family.
"We place a high value on openness with all our foster carers, share information about any risks with them from the outset and continue to keep them informed. This was our approach with Mr and Mrs Jones."