Living in Google's world means giving it a lot of your data, so it's important to take a peek at your privacy settings from time to time. You can't do that in Google Pay right now without a lot of leg work. A botched system update on Google's end has apparently hidden the privacy settings from most users, but Google is working on it.
The Google Pay settings page in the Payments Center should have a section for privacy at the bottom under "Users," but it doesn't. The section includes settings that allow Google to use your credit data, market to you based on personal information, and tell third-party sites you visit whether or not you have a Google Payments account. All three options default to "on."
If you want to turn those off right now, you have to use a direct link to the sidebar section at https://pay.google.com/payments/u/0/home#settings. Google confirms that the privacy options should be visible when you navigate to the settings page manually. It's working on a fix that will make the settings show up, but notes the direct link is available in the Google Pay privacy notice. What? You don't read the privacy notice on a regular basis?