Gray pop up windows in Mail

Clear all history and website data , do you use any extensions remove them Change Extensions preferences in Mail on Mac - Apple Support

Clear your browsing history in Safari on Mac - Apple Support

Manage cookies and website data in Safari on Mac - Apple Support

Right click on the url and follow these settings .

Change Viewing preferences in Mail on Mac - Apple Support

Follow Change Websites preferences in Safari on Mac - Apple Support

Customise settings for each website in Safari on Mac - Apple Support

Hello David Gurga,

We understand you have an issue with pop up windows in the Mail app on your Mac. We'll do our best to assist with this.

Are you referring to the look up feature or pop up window when you hoover over the link and select the drop down option? It browses online for the link or photo. However, you would have to select that drop down option to see this pop up window.

We'd recommend isolating this behavior further with these steps:

1. Quit the Mail app from the Mail menu > Quit Mail. Relaunch it and test it out.
2. Test safe mode with these steps: How to use safe mode on your Mac - Apple Support Use sections, 'If the issue continues in safe mode' and 'If the issue doesn't continue in safe mode', depending on your results there.
3. Add a test Administrator user on your Mac. Log out of the current user and into the test user to see if the issue continues there:Set up users, guests, and groups on Mac - Apple Support

If the issue is specific to your user, you can try to relaunch the Mail app while simultaneously holding down the Shift key as it loads up. Release Shift key once it has opened completely. This should remove the app's saved state.

Let us know how it goes, cheers.

See the article Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

How to identify fraudulent emails and messages

Scammers try to copy email and text messages from legitimate companies to trick you into giving them your personal information and passwords. These signs can help you identify phishing emails: 

• The sender’s email or phone doesn’t match the name of the company that it claims to be from.
• The email or phone they used to contact you is different from the one that you gave that company.
• A link in a message looks right, but the URL doesn’t match the company’s website.2
• The message looks significantly different from other messages that you’ve received from the company.
• The message requests personal information, like a credit card number or account password.
• The message is unsolicited and contains an attachment.

Don't download this link , simply delete the fraudulent mail to trash and empty the trash from apple mail application Safety tips for handling email attachments and content downloaded from the Internet - Apple Support

Hi David Gurga,

Thanks for the reply and screenshot! While there's not a way to disable the link previews you're showing, we always welcome feedback. If you'd like to submit a suggestion, you can do so with this link: Product Feedback - Apple

Take care.

For normal working mail app these pop ups never appear , create a new admin account in users and groups and configure mail accounts , check if this pop up once again occur .

Set up users, guests and groups on Mac - Apple Support

Add email accounts in Mail on Mac - Apple Support