The tension reached breaking point as the gunmen holding her and her parents, Hugh and Helen, were preparing to make a video stating their demands and Ms Burton, 24, was urging them to release the family.
In her first detailed account of the 58-hour ordeal to three British newspapers, including The Independent, she said: "The situation was starting to get very tense. Maybe they felt they hadn't achieved what they wanted. They began getting nervous and started shouting at me.
"One of the two main guys said: 'I can't believe you have been so disrespectful - we have given you blankets, we have given you food, we have treated you so well'.
"I got really mad and said: 'I can't believe you're doing this. Do you want me to get down on my knees and say thank you, thank you, thank you, thank you?' I was exhausted and started crying. I said: 'I came here to work with the Palestinian people and now I feel I have been stabbed in the back.'"
Ms Burton made it clear that this was one of the few occasions when the kidnappers behaved in anything other than a calm, even hospitable, way towards their victims after seizing them at gunpoint - or in which her own remarkable self-possession briefly cracked.
She said that from the time they arrived at about 4.15pm last Wednesday at the first of three Gaza safe houses, "they tried to make us feel at home in the Arab style. They offered us tea, coffee, water, chocolate, popcorn. You don't want to co-operate with them by accepting, but then you feel guilty because they have been so kind - overlooking the fact, of course, that they have kidnapped you.?
She admitted that she had e-mailed British diplomats about her parents' impending trip to Gaza and had been referred to last month's travel advice from the Foreign Office, advising Britons against all travel to Gaza. Ironically, she had wanted to use her parents' 24-hour trip to Gaza to " show them the good side of the Palestinian territories and to reassure them that she was relatively safe working in Gaza".
She added: "I feel really guilty. I feel irresponsible. I'm the one who lives here and should have known better. I have given them their worst Christmas and holiday ever. Luckily nothing happened but it might have."
While the emotions of all three Burtons had gone "up and down" during the ordeal, they appear to have kept their composure to an impressive extent, although her parents had both said that this would be their last trip to Gaza.
The kidnappers offered the family packages of new clothes. Although the family were reluctant to accept them, Ms Burton said: "My mother put on the trousers and told the guys she wanted to wash her knickers. Then she asked one of them to hang the knickers up on the line outside the house. She embarrassed him a bit. He blushed a bit, but put them up on the washing line. "
Despite her reluctance to accept creature comforts from the kidnappers, she had finally applied a little toothpaste with her finger while eschewing the offer of a toothbrush. The family had become "pretty scummy" by the end of the ordeal, she said.
She explained that they had been moved twice at night, first on Thursday to a house in southern Gaza five minutes away from the first one, and the second time on Friday night - after a power cut which delayed production of the kidnappers' video - to a third house either in Gaza City or northern Gaza.
She said that her father had been "irritated" on the first day and had repeatedly stressed to the kidnappers that he and his wife had a flight to catch. He had also asked them whether they realised that the Erez crossing from Gaza into Israel closed at 9pm.
Ms Burton's account - which is the fullest and most graphic from any of the victims of the series of kidnaps in Gaza over the past year - appeared to reflect her own conflicting feelings of guilt about exposing her parents to the ordeal and her anger towards the kidnappers themselves - but laced with an element of sympathy towards what she saw as the desperate conditions in which they live.
Ms Burton said she felt "sorry for the guys" because of their "shattered lives", and the fact that they were, in effect, on the run and had family members who had been killed in the conflict.
But, at the same time, she added: "I can't forgive them for what they did and I hope they don't keep doing it in the future. I understand that the majority of the Palestinian people are not like them."
Ms Burton emphasised that she wanted to continue working in the occupied territories, but would "assess her options" about where she would work. She admitted that she was a "bit worried about personal security" in the event of a return to Gaza, but added that the security crisis would only be solved with the end of Israeli occupation and a viable economic future for the strip.
She added: "I definitely want to stay working with the Palestinian people one way or the other"
Adding that Palestinians in Gaza were living in "disgusting conditions" she declared: "I've never met people like the Palestinians. They're the strongest people I've ever met. I would feel kind of guilty turning my back on them. I think it's awful what the kidnappers did, but it made me even more impressed with the Palestinian people - how they rallied together to try and get us out."
While Ms Burton, who speaks Hebrew and Arabic, is strongly pro-Palestinian, she added: "I have a lot of Israeli friends. I speak their language and I try not to get too involved. You have to stand back and see there are two sides to every issue."
She said the kidnappers - who had apparently tracked the Burtons during their tour of Rafah - told the family they had a made a mistake. "They said they thought we were Americans," Ms Burton said. "But when I said you have made a mistake, so why not let us go, they said it was too late." The kidnappers told the family repeatedly that they would be released unharmed "in a few hours".
Ms Burton said she now had worried about the impact of the kidnappings on European election monitors due to oversee Palestinian elections this month. But while the monitors had been threatened in the videotape, she said the kidnappers, who were strongly "pro-Arafat", had been preoccupied by what they saw as the failure of Palestinian President Mahmoud Abbas to press Israel to allow voting to take place in East Jerusalem.Reuse content