Put link/button in email to reply to sender on website
I don't think you can do this from webform alone.  I would create a custom form (using Form API in a custom module) with a path that includes a parameter to identify the original webform submission.  Something like /quote-response/{webform-submission}.  The "response form" then queries the webform submission to get the email of the person who submitted the original quote request.  Keep in mind if this route doesn't require any authentication, you could be opening yourself up to bots / malicious users, so I recommend implementing some additional security / verification.