I was able to resolve the issue in so that emails would be sent from my own email address and the replies would go to the user’s email.
To do this in ContactForm7:
1) Set the “From:” to your email
2) In the “Additional Headers:” section, enter “Reply-To: [your-name] <[your-email]>”
Do note that Gmail ignores the Reply-To when you reply to a message containing a “Reply-To” as described at https://productforums.google.com/forum/?hl=en#!category-topic/gmail/composing-and-sending-messages/ZRZA5KkTPAA . Gmail does not appear to be an issue if you are using another email client to access a Gmail account though.
