It seems to be the MTA (probably the spam filter), since it happens to me even without any client open, so there's probably no way to close it by your end.

If it happens without any client open, then it isn't really a problem is it?

Well, it doesn't happen if the address doesn't exist (I tested it too), so it can still be used by spammers to check for that.

If an address doesn't exist the message will simply bounce. Or am I missing something?

Yes, here is an example of an address that doesn't exist:

https://grepular.com/email_privacy_tester/lookup?code=gapz72...

If the address exists in Gmail, you get a response on "DNS Prefetch - Anchor", so it could be used to determine whether to send an email or not. I'm not a mail administrator but I can imagine how it might be useful to a spammer, e.g to stop mass bounce replies.