(CBS) -- Michael and Kelly Gallivan say the first un-ordered package arrived in October...
"I went out and picked up the package and Mike's name was on it. I opened it up and I said what did you buy this stuff for? And he said- I didn't buy that!" Kelly says.
They say that was a phone charging hand warmer, and it was soon joined by a humidifier, a flashlight, a Bluetooth speaker, a computer vacuum cleaner and some LED lights.
The couple says they had no idea where the packages are coming from.
"We did not know. I called Amazon, and what I wanted to do was I wanted to like send it back. They said to me what's the order number. I said I don't have an order number because I didn't order the thing," Michael says.
The merchandise comes without any return addresses.
The scam is known as "brushing." An online seller – usually overseas – purchases their own products through fake buyer accounts they've created. The products are shipped to a real address. Then, the seller writes a positive review of their items from the fake buyer account.
"The positive reviews are like gold …People are always looking for a new hole in the structure at Amazon to be able to put more fake positive reviews on them," says retail security expert Brian Kilcourse.
In a statement to CBS This Morning, Amazon said they investigate every report of customers receiving unsolicited packages and "will ban all vendors and reviewers who abuse the reviews system."
Michael and Kelly say getting the packages is so disturbing because...
"It indicates that information that's very close to us, about us is out there circulating around the world."