1) Navigate to the various emails within the instance and un-approve them. May require removing references to the email first.
2) Re-approve the emails.
3) Add back any references to the email asset.
Why this needs to be done:
When the email asset is approved it goes through a validation process for all the tokens that are used and this includes the global unsubscribe settings. When editing in Admin >Email > Unsubscribe the validity of tokens is not checked upon saving those changes. If a invalid token is added, something like {{lead.nonExistingField}}, no errors are thrown and it'll return that string value. The verification is done when the "approve" email functionality is used on email assets. This steps retrieves valid tokens list used in the email and adds/updates them in a backend table for use/reference. The update to the global unsubscribe settings doesn't cause the stored information to reference the newly changed settings in Admin. To cause that validation process to go through successfully and update the information on the back end, you'll need to un-approve and re-approve the various emails within the instance to use the new global settings.