Nassly Sales said she ordered two boxes of diapers from the site's Amazon Warehouse section - where open-box and returned items are sold at a discounted rate.
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She said the package arrived this week, but when she opened it, some of the diapers appeared to be soiled.
"I picked up the diapers and it was a little bit heavy. I was half asleep and the lights were off. At that point, I turn on the light and that's when I noticed these diapers are neatly-folded and they are soiled," Sales said.
Sales said she disinfected their nursery and wiped down her 19-month-old daughter, who was born premature, with rubbing alcohol.
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The family said they have not tested the substance, but that it looks and smells like feces.
Amazon's website says the company inspects and certifies all open-box products before re-selling them.
In a statement, an Amazon spokesperson said, "we are investigating the situation and in contact with the customer to make it right."