The link have question mark in the middle and a unique identifier behind it. When a web browser requests the website from youtube, it will look at that identifier and know that link was generated by a specific user. If you request the video while logged in then google knows that those two accounts are somehow communicating. If over time two youtube accounts are communicating bidirectionally then they are probably friends. If communication is going only one way then it might be an influencer account.

Removing that identifier will remove information about who sent you the link.