Use your email client’s normal Reply action on a forwarded message. AnonAddy puts a reply address in the message headers so the response can be routed through the alias.
The message must be sent from a verified recipient on your idler.me account. If it comes back to you, check the From address in Sent and verify that the account address is the one registered with the service.
The recipient will see the alias as the sender, not your verified destination address. OpenPGP keys and signatures can be removed during reply/send processing to avoid exposing an identity in a public key.