I used the verified email option instead of SMTP.

I used the verified email option instead of SMTP. When the autoresponder message is received it includes "via jotform.com." I'd like to get rid of that. (I'd also like to get rid of that when someone saves their data to continue later). If I use SMTP will that eliminate the "via jotform.com" when the user receives the autoresponder message?

Yes, if you use SMTP, it will remove "via jotform" when the email is sent.

Unfortunately, for save and continue later email, it will not change since the verification emails are sent from our email servers (noreply@jotform.com).