The corporation said it had not been informed of the teenager’s family connection in advance by the film’s production company.
The BBC’s board is expected to discuss the film on Thursday.
The letter, sent to director-general Tim Davie, BBC board chair Samir Shah, chief content officer Charlotte Moore, and CEO of BBC News Deborah Turness, said the film offered an “all-too-rare perspective on the lived experiences of Palestinian children”.
It reads: “Beneath this political football are children who are in the most dire circumstances of their young lives. This is what must remain at the heart of this discussion.
“As programme-makers, we are extremely alarmed by the intervention of partisan political actors on this issue, and what this means for the future of broadcasting in this country.”
The letter’s other signatories include directors Ken Loach and Mike Leigh, actors Khalid Abdalla and Ruth Negga, musician Nitin Sawhney and Sara Agha, who presented the BBC documentary series The Holy Land And Us: Our Untold Stories.
A BBC spokesperson said: “Gaza: How to Survive a Warzone features important stories we think should be told – those of the experiences of children in Gaza.
“There have been continuing questions raised about the programme and in the light of these, we are conducting further due diligence with the production company. The programme will not be available on iPlayer while this is taking place.”
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