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The airline - which also hit headlines when MH17 was shot down over eastern Ukraine in July - invited travellers from New Zealand and Australia to enter the competition, which kicked off on Monday and offered them the chance to win an Apple iPad or return trip to Malaysia.
They were asked to answer the question, "What and where would you like to tick off on your bucket list, and explain why."
Mrs Weeks, whose New Zealand husband Paul was one of 239 people lost when Flight MH370 disappeared in March, said she was "blown away" by the airline's insensitivity.
The Perth mother of two said many of the airline's interactions with families of the victims were "insensitive".
"This is just another promotion that they've come up with. It's just atrocious - why would you say that?
"We're sitting here wondering [and] they've been entrusted with our loved ones and can't tell us where they are."
Auckland University senior marketing lecturer Bodo Lang said Malaysia Airlines had made a "very poor choice from an advertising stand point".
"Other airlines would have got away with this but Malaysia Airlines should have shown ... awareness in this situation.
"Competitions are an often-used tactic in many product categories. Travel is no exception and the idea of being able to win a trip to an amazing location lends oozes [of] positivity and that is exactly what Malaysia Airlines needs at this point. And passengers, of course."
The competition was not going to help the airline's reputation, Dr Lang said.
"They have had two fatal incidents in one year. While Malaysia Airlines may have had very limited control over why these incidents happened, they were in control over how they handled the aftermath and this could have been handled much better.
"In the long run, Malaysia Airlines will have to gradually rebuild its trust with passengers and the public. The unfortunate naming of the competition would have made this task again more difficult for the airline."
Last night, Malaysia Airlines issued a statement saying it had "withdrawn the title of a recent competition available to Australia and New Zealand ... as it is found to be inappropriate at this point in time".
"The competition had been earlier approved as it was themed around a common phrase that is used in both countries. The airline appreciates and respects the sentiments of the public and in no way did it intend to offend any parties."