Stripe automatically enables Link in the Card Element for all businesses with granted access (no code changes are required). If you want to turn Link off for all instances of the Card Element, visit the Link section of your Payment Method settings >> disable the Link in Card Element setting. This setting applies to both forms of the Card Element.
To selectively disable Link in the Card Element, use the disableLink parameter. You only need to use one of these controls—if either disableLink is true or Link in the Card Element is disabled in settings, Link won’t appear in the Card Element.