Due to the last minute nature of the pair's nuptials, which took place at the fabled A Little White Wedding Chapel on May 1, they used a Ring Pop Sours as a temporary stand-in for a more permanent ring.
Elvis Presley impersonator Jesse Garon officiated the wedding, and found the wrapper while he was being interviewed about the ceremony by U.S. TV show Entertainment Tonight.
Seizing his opportunity, Garon then put the wrapper on the U.S. auction site - with the bid standing at $4,050 (£3,090) as WENN went to press.
As well as getting the "slightly used" wrapper if they win the auction, the victor will also receive a copy of the moment Garon found the trash, in addition to a "certificate of authenticity" signed by the minister.
To further encourage bids on the item, Garon states in the description it is "a great gift for the Jonas Brothers fanatic the has everything (sic)."
Fans clearly agree with him, as the lot already has a staggering 82 bids - with seven days still left in the auction.
According to reports, "Game of Thrones" star Turner and her singer spouse decided to go ahead with the Vegas wedding in a bid to make their union official in the U.S. before they celebrate with a larger ceremony in France later this year.
Their Sin City nuptials took place just hours after the Billboard Music Awards, with the date also the same day late singer Elvis married wife Priscilla Presley 52 years previously.
Asked about the tribute, Priscilla Presley acknowledged it was "very sweet, really, really, very sweet," during a chat with Us Weekly magazine.