Google's mail server is rejecting the message because, it would appear, that Google doesn't know they're supposed to be the authoritative recipient of those messages. The "clue" is the mention of relaying in the error message. That means that the recipient server is "seeing" the message as a relay attempt, not a local delivery attempt.
Are you certain that Google's service is configured for the correct domain name and all paid-up, provisioned, etc?
So you have been hit by a spam protection mechanism. First you have to find out, wether the email(s) get rejected for good reason. Does your customer send explicitely solicited emails only, or does he - sometimes - send work proposals to people who have not asked for this service? If he does send unsolicited emails, he has to stop that, before the situation can change.
As soon as that's sorted out, you may check the technical situation. The system qproxy1.mail.unifiedlayer.com uses an IP address to send mail to other mail servers. Check, wether this IP is blacklisted somehow by using one of the many RBL checking services you easily find searching for "rbl check". If it is blacklisted, follow the blacklist's instructions to get removed. Each blacklist's policy is different, but basically they all tell you the reason for their blacklisting and require to correct the situation.
If your server is not found on any public blacklist, check at AOL.com for their "IP reputation service": https://postmaster.aol.com/ip-reputation - if you are listed there, follow their instructions, including subscribing to their feedback loop system. Use it! They won't care about your problems unless you have been verified using it.
IF YOU ARE SURE your customer's emails are 100% clean, I mean really 100% of 100% clean, so any spam complaints are 100% nonsense - not a single one is for good reason - THEN YOU MAY CONSIDER routing your customer's mails through anoter mail server, which is not blacklisted, until the blacklisting is removed. This may take some weeks! But if there are reasonable complaints, your other mail server will be lacklisted instantly.
I had such a blacklisting some time ago when I started using a new leased root server for mail services. The IP my hosting provider uses was blacklisted at AOL, because a former client of my provider had been sending spam without my provider knowing it. When this customer left, the IP was reassigned to a new server, but it remained blacklisted at AOL, so it hit me. It took some time (about two weeks), but I got it unlisted.
Spam protection is trickey. Some recipients have asked for being subscribed to a mailing list, but later they decide otherwise. Instead of unsubscribing they mark your mail as spam and get rid of it this way. Then their provider rejects your legitimate mails as spam, and if there is more than one such recipient, they may start blacklisting your mail server. This is a common scenario you have to check for.
There are many other possible reasons for your customer's emails getting rejected, but do these checks first - most probably that's all you need to do.
Good Luck! TomTomTom
Best Answer
Not everyone uses MX records for their e-mail, so servers expecting A records to resolve to a usable mailhost (where there is none) will still get bounces.
Also, 48 hours is not always long enough for all caching servers to update, though it should be enough time...