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 occupied territories and Gaza.
It is unclear when the video was shot.
.
In a statement, the Qassem Brigades said the woman was an Israeli settler.
“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.
An estimated 150 captives were captured by Hamas on Saturday during its unprecedented assault on Israeli occupied territories, which immediately declared war on Gaza.
The relentless Israeli bombing over five days has killed more than 1,200 people, including women and children, and wounded more than 5,000 others in Gaza, its health ministry says.
The United Nations Palestinian refugee agency says at least 340,000 Palestinians have been displaced across Gaza, creating what observers say is a “humanitarian catastrophe”.