I can reply yo emails. It's what jaybone said -- I use a 3rd party outbound (SMTP).

I use Thunderbird as my mail client. In there you can define multiple IMAP/pop accounts (inbound) and multiple SMTP (outbound). So when I click reply, the SMTP I have set for that email address is a 3rd party service that sends emails using my domain.

This does have a privacy implication, so whether that's appropriate for you is for you to decide. The 3rd party can read and save a copy of your outbound email inclusive of any content included with it (like the email you're replying to if you include it).

Maybe they send emails using someone else’s smtp server? (Like some paid service that provides smtp?)