It's a ritual for millions of caffeine-laden Canadians: After every last drop of coffee has been drained from the cup, the soggy paper rim is pried open in the hopes winning a prize.

Like so many other Tim Hortons aficionados, Ally Fraser has always relished the arrival of the annual Roll Up the Rim contest, but a central component in the draw has become hard to swallow for the self-described environmentalist.

Each time a coffee lover seeks a prize, another paper cup ends up in the landfill.

Fraser, a 24-year-old from Beaumont, Alta., started thinking about the environmental impacts of Canada's Tim Hortons addiction last year.

"I'm standing in line with my reusable mug and it's roll up the rim time. So I'm faced with this internal dilemma: Do I continue to make the green choice and use my mug or do I take the paper cup for my chance to win a car or TV?

"I make the choice, I take the paper cup, and I'm wracked with guilt because I'm thinking, if I'm making this decision, how many other people are making this decision?"

Fed up with having to choose, Fraser started a petition asking the restaurant chain to give reusable mug owners a chance to play. After sitting largely idle for months, the petition is finally getting some buzz.

"In the last 24 hours I've got 16,000 signatures, and I'm so happy that people agree with me that this needs to be changed," Fraser said.

'We don't get an equal chance to play'

Tim Hortons says it will issue at least 272,598,720 cups this year. Fraser crunched the numbers and estimates that 15 million of those cups are used by people making the switch from reusable mugs.

"I realized that this is a much bigger issue than I originally thought — and I thought maybe other people are facing this dilemma and maybe I should do something about it."

Fraser started her petition during the 2015 contest season, but it garnered fewer than 100 signatures. When Fraser submitted it to Tim Hortons management, she was told that changing the draw to include new contest forms would end up being more wasteful.

"Last year was frustrating for me because it seemed like Tim Hortons thought this was not a cause that was worth looking at, and now that people agree with me, maybe this year they'll actually listen," Fraser said.

Although Tim Hortons offers a way for contestants to play at home with a receipt, the online contest is a separate pool and contestants don't have access to the same prizes.

"To me, that's kind of a cop-out, because everybody can win the online game; they don't have to buy coffee to play," Fraser said.

"We do have a chance to play with a reusable mug, but we don't get an equal chance to play."

Fraser says Tim Hortons should be offering incentives to people who choose to drink their coffee from reusable mugs; those who want to ditch the paper cup could be given a small sticker or scratch card to take part in the contest.

CBC News has contacted the Tim Hortons head office for comment.