The Gmail to Evernote script works by sending a message to your Evernote email address. It does so using Google Apps Script. Until recently, a message sent by Google Apps Script would not appear in your Sent mail; in many cases, this would be considered an omission, and it has been fixed now: the messages will show in your Sent mail.
For messages sent to Evernote, keeping a copy in your Sent mail is less relevant; several people, including myself, considered it a benefit that these message were not cluttering your Sent mail. I will therefore look into the options for not getting receiving a copy of the mail to Evernote in your Sent mail, perhaps as an option that you can switch on or off. No immediate solutions have come to my mind yet, but if I get some, it will be implemented in the next version.
Meanwhile, any bright ideas are welcome!
Update: the bright idea is to create a filter in Gmail, specify your Evernote address in the To field of the search criteria, and select Delete it as action (submitted by Nathan Stretch, comment below).