Google Scholar Button doesn't collect or transmit any information if you don’t actively use it.

When you click the button, it requests data about the currently visible webpage from Google Scholar. The request includes the current webpage's URL, title, and other bibliographic information; the text you have selected; and, if the webpage is a search engine, your current search query. It also includes the user agent, IP address, and account information just as if you had visited Google Scholar in your browser.

If the current webpage is an article, or if you have selected a reference to an article, Google Scholar responds to the request with data about this article such as its citation count, related articles, and how to cite it in several formats. If the current webpage is a search engine, Google Scholar responds to the request with its search results for your current search query. It uses the user agent, IP address, and account information from the request to compute and format the response just as it would if you had visited Google Scholar in your browser. For example, it uses the IP address and account information to identify and include your library subscriptions.

Google Scholar’s operation is covered by the Google Privacy Policy: https://www.google.com/policies/privacy/.