The pet bird was terrified by the noise when the Hercules transport aircraft roared over its owner's house.
Its death in Ayrshire followed a similar incident where a low-flying plane caused a parrot to fall off its perch and break both its legs. Military chiefs agreed to cover vet bills - including two splints.
Both cases were among 200 separate claims for damage caused by low-flying military aircraft in the past three years. They left the Ministry of Defence with a 1.4 million pounds compensation bill, the Daily Mirror reported.
"We are very aware of the risks of military flying and the safety of those on the ground, as well as our air crew, is one of our highest priorities," the spokesman said.
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Other settlements included 300 pounds to two therapy groups disturbed by fighter planes overhead and 900 pounds for damage to a child's trampoline in Lancashire.
Much larger sums were paid out for personal injuries and damage to livestock, buildings and crops, the MoD said.
Chicken farmers have also been given payouts after they claimed aircraft noise affected their birds' ability to lay eggs.
The MoD said a plane was classed as flying low if it was at less than 2,000 feet above the ground or 500 feet for helicopters.