Yasemin Kara, a cousin of Atkinson - who left the show at the Judges Houses’ stage of the show - set up the online petition asking for the 32-year-old landlady to be reinstated.
Atkinson left after Honey G, real name Anna Georgette Gilford, was put through to the live stages by Overs category mentor Sharon Osbourne, who said she had decided to take a “risk” on the 35-year-old.
She also chose Saara Aalto, 29, from Finland, and Relley C, 26, who was turned down by Nicole Scherzinger in the Judges’ Houses segment of a previous series. Three other acts were sent home by Osbourne.
Ms Kara appealed for people to sign to “show X Factor bosses and ITV that they have made a huge mistake”.
Atkinson appeared to distance herself from the petition, telling BBC Radio Humberside that Honey G “deserves her right to be in the competition as much as anyone else”.
She added that the pair had become “friends” during their time on the show together.
Set up on Sunday night after it was revealed Osbourne would be taking Honey G through to the live shows, the petition adds: “Samantha Atkinson is my cousin and I and thousands of other X factor viewers feel she was robbed of her place on live shows tonight, when Sharon Osbourne gave Honey G one of them places in final 12.”
The petition had received 8,300 signatures by Tuesday morning.
Honey G, who is in the over-25s category, has sparked speculation that she is not genuine because of her amusing dance moves, outfits and attempts at street slang.
During her earliest audition, judge Simon Cowell told her: “You shouldn’t be doing that!” adding: “Please, please just end this.”