We've discussed the two methods that you can use to attach your EBC to a message: Attach it one message at a time by using the Business Card button, or attach it to every message by including it in a signature. Either way, when you attach your EBC to an e-mail message you're creating, you're making a unique copy of the EBC for that message or that signature only.
If you need to make a change to the information that appears in the business card you've attached, you'll need to follow these steps:

Delete the attached business card and the .vcf file from the message (or delete the card from the signature if you used that method).

Return to Contacts, and make the revisions from there.
Then, once you've saved the changes, re-insert your EBC in the message or in the signature.