If you can login:
On the website, click the icon in the upper left corner and then click Account (theathletic.com/settings). You can change your Email or Password under Account.
On the app, tap the button in the top left corner, and then the button next to “My Feed”. Tap the Pencil icon overlapping your profile image to change your Name or Email, or to link your account to Facebook. You cannot change your password in the app at this time.
If you can't login:
Change your password at theathletic.com/forgot-password and then move on to the steps detailed above. Resetting your password at the link above will remove your Facebook data as well, so if your workplace blocks Facebook Login to The Athletic, you can reset your password to remove the FB data and sign in using Email/Password at work.