Travellers have been sharing images of the napkins, which feature an array of messages encouraging fliers to flirt with fellow passengers, on Twitter.
"Be a little old school. Write down your number and give it to your plane crush. You never know..." reads one napkin.
Another says: "Because you're on a plane full of interesting people and hey... you never know."
There are even dedicated spaces on the napkins for people to write down their name and phone number.
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Delta has collaborated with Diet Coke for some time, but the latest napkins have generally not gone down well.
"These napkins are creepy AF," one person wrote in a message to both brands.
"Pretty sure no one appreciated unsolicited phone numbers in the 'good old days' and they sure as heck don't want the number of someone who has been gawking at them on a plane for hours today. Not a good look."
Another woman called the napkins "awful."
One Twitter user pointed out that although the effect may not have been planned, the napkins were indeed "unintentionally creepy."
Delta has since apologised for "missing the mark."
"We rotate Coke products regularly as part of our brand partnership, but missed the mark with this one," a Delta spokespeson told INSIDER. "We are sorry for that and began removing the napkins from our aircraft in January."
A Coca-Cola spokesperson also told INSIDER: "We sincerely apologize to anyone we may have offended. We worked with our partners at Delta to begin removing the napkins last month and are replacing them with other designs."
