The footage aired on Al Jazeera on Wednesday night was shot from a distance, showing the unidentified woman and the children from behind.
The men, presumably Hamas fighters, are seen walking away after leaving them in an open area near a fence, which could be the frontier between Israel and Gaza.
It is unclear when the video was shot. The Israeli authorities are yet to comment on the video.
In a statement, the Qassem Brigades announced the woman was an Israeli national.
“An Israeli settler and her two children were released after they were detained during the clashes,” said the statement, according to a report by the AFP news agency.
Al Jazeera’s Hoda Abdel-Hamid, reporting from West Jerusalem, noted the Israeli media is treating the video with a “pinch of salt”.
“One reporter said Hamas was in damage control, and that it was a media stunt. Other Israeli channels are saying this release happened earlier. Some are saying it happened on Saturday and that Hamas is trying to improve its international image at this point in time,” she added.
“The pictures are still spreading around the country, it’s just been aired on Al Jazeera, people are just trying to digest what they have seen,” she continued, adding that there have been “conflicting” reactions so far.
An estimated 150 captives were captured by Hamas on Saturday during its unprecedented attack on Israel, which immediately declared war on Gaza.
The relentless Israeli bombing over five days has killed over 1,200 people, including hundreds of civilians, and wounded more than 5,000 others in Gaza, its health ministry has confirmed.
The United Nations Palestinian refugee agency says 250,000 people have been displaced in the Palestinian enclave put under a total siege by Israel, creating what observers say is a “humanitarian catastrophe”.
The Israeli military says more than 1,200 people, including 155 soldiers, have died in Israel since Saturday.