Her brother Gordon, 19, was killed in Basra on 28 June when the jeep he was travelling in came across a roadside bomb.
He was sent to Iraq just a few weeks after finishing training for the 1st Battalion Royal Highland Fusiliers.
Maxine's mum, Rose Gentle, walked out on the meeting with Mr Prescott saying he was "talking rubbish".
Mrs Gentle is understood to have been very angry that the letter from Mr Blair took so long to arrive.
Maxine and her mother were joined at Downing Street by members of the Stop The War coalition and anti-war Labour MP Jeremy Corbyn.