"Wir laden den Anhang der E-Mail nicht herunter."
Translation:We don't download the attachment of the email.
Why couldn't you said "from the e-mail" as well since that implies the same relationship?
I mean, strictly speaking, it's probably the same situation, but I interpret "from the email" as being the source of the download and "of the email" as establishing a relationship between the email and the attachment.
So I could say "I'm not downloading the attachment from the email" (but am downloading it from somewhere else), which would be slightly different from not downloading the file that is attached to the email (the attachment of the email) at all.
I'd also probably just say the email attachment (or maybe the email's attachment) rather than the attachment of the email, but that's really more of a flow thing that a correct/incorrect thing.