Amazon has a beef with the start-up PayPal recently acquired, Honey.

During the height of the holiday shopping season, the e-commerce giant warned some users that the browser extension could be a "security issue."

"Honey tracks your private shopping behavior, collects data like your order history and items saved, and can read or change any of your data on any website you visit," the message, which was posted on Twitter by multiple users, said. "To keep your data private and secure, uninstall this extension immediately."

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PayPal paid $4 billion for Honey in December — the largest acquisition in the payment company's history. The Los Angeles-based start-up was founded in 2012, and lets users find coupons while shopping online. It works through a browser extension known as a "plug-in" that automatically searches for discounts as customers shop on sites like Amazon. Honey makes a commission off each sale and has ushered in 17 million users.

PayPal and Amazon haven't historically worked closely together. PayPal was once a part of Amazon competitor eBay, and Amazon does not accept PayPal as an option in check-out. It also has a competing discount plug-in.

Honey's plug-in has been compatible with Amazon since it hit the market roughly seven years ago. This appears to be Amazon's first public scrutiny of the start-up for security concerns.

"Our goal is to warn customers about browser extensions that collect personal shopping data without their knowledge or consent such as customer name, shipping and/or billing address and payment method from the checkout page," an Amazon spokesperson told CNBC.

A spokesperson for Honey said the extension "is not — and has never been — a security risk and is safe to use."

"We only use data in ways that directly benefit Honey members — helping people save money and time — and in ways they would expect. Our commitment is clearly spelled out in our privacy and security policy."

The company said it collects "limited shopping data" and uses it to analyze information on retail websites so users can find the best coupon, but does "not sell your personal information. Ever."