Southwest Airlines is giving passengers on board the disastrous flight which saw a woman die when she was sucked out of the window this week US$5,000 ($6,935) each and a US$1,000 travel voucher.

The airline's CEO Gary Kelly sent a letter to the 142 passengers who survived, apologising for the "circumstances" which surrounded the flight and offering their help reuniting them with luggage.

No blame has been assigned to the airline for the engine explosion which sent a piece of shrapnel flying through the window next to Jennifer Riordan, according to the Daily Mail.

It caused the window to smash and Riordan, a 43-year-old mother-of-two was partially sucked through the hole in the plane and died as a result.

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Investigators are still probing what caused the explosion and the plane had been tested for safety just three days before the catastrophe.

In its letter, Southwest Airlines pointed to the ongoing National Transport Safety Board investigation into the incident but said its priority was assisting the traumatised survivors.

"On behalf of the entire Southwest Airlines Family, please accept our sincere apologies for the circumstances surrounding Flight 1380 on Tuesday morning April 17th.

"While the National Transportation Safety Board continues its investigation as to the circumstances surrounding the accident, our primary focus and commitment is to assist you in every way possible.

"We value you as our customer and hope you will allow us another opportunity to restore your confidence in Southwest as the airline you can count on for your travel needs.

"In this spirit, we are sending you a check in the amount of US$5,000 to cover any of your immediate financial needs.

"As a tangible gesture of our heartfelt sincerity, we are also sending you a US$1,000 travel voucher which can be used for future travel.

"Again, please accept out heartfelt apologies."

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There were 143 passengers on board the plane including Jennifer Riordan. The airline would not answer DailyMail.com's questions about what it had offered her family in the way of compensation on Friday morning.

A spokesman would only confirm the compensation, telling DailyMail.com: "Ours is a company and culture built on relationships.

"We can confirm the communication and gesture are authentic and heartfelt."

It is also unclear if they are giving the five crew, including hero pilot Tammie Jo Shults, anything, or if the US$5,000 check applies to every single passenger, every family, or every person over the age of 18 who was a passenger.

In total, it means to the airline is giving less than US$1 million to the other passengers.

Riordan's family said earlier in the week that it was too soon for them to consider any form of legal action against the airline.

None of the passengers who survived the flight have made any form of complaint against the company either.

Most are grateful to be alive and say they thank Southwest's crew, namely pilot Tammie Jo, for ensuring they got to the ground safely.

Andrew Needum, the EMT who tried to save Riordan's life by pulling her body back into the aircraft, said he was in 'no doubt' who he would be flying with in future.

Hollie Mackey was sitting in the same row as Riordan when the upper half of her body was sucked out the window.

There was a little girl in between them and she and the child tried to pull her body back into the aircraft but were not strong enough.

Needum and Tim McGinty were able to together.