Unix time (also known as POSIX time or Epoch time) is a system for describing instants in time, defined as the number of seconds that have elapsed since 00:00:00 Coordinated Universal Time (UTC), Thursday, 1 January 1970, not counting leap seconds. It is used widely in Unix-like and many other operating systems and file formats.
I use the tool at Epoch Converter to convert variables where I can't use PHP date("U")
It's not difficult, keep in mind that you may derail old conversations that contain important data that increases your search engine ranking for pages, but the request was how do I, not why shouldn't I...
Go ahead and open the "Member Management" link ("Members" in v7.6+) in the Control Panel and select Advanced and then select "before" and choose a date for the "Last Post Date" or "Last Online" (keep in mind, quite a few users have account on forums and don't post; myself included) and click search. On the results page you can select "Delete" from the "Actions" area (bottom of the results page) to prune those users shown.
Any error messages from remote servers will be contained within our mail log; example (the server IP and system response key has been removed from the below example):
ECDHE-RSA-AES128-GCM-SHA256:128 CV=yes: SMTP error from remote mail server after end of data: 550-5.7.1 [systemip 7] Our system has detected that this message is\n550-5.7.1 likely unsolicited mail. To reduce the amount of spam sent to Gmail,\n550-5.7.1 this message has been blocked. Please visit\n550-5.7.1 https://support.google.com/mail/?p=UnsolicitedMessageError\n550 5.7.1 for more information. responsekey.176 - gsmtp
The above error links to the Error Message page at Google. "Trusted" sites have a reverse DNS on their IP addresses (which must be done through your webhost, generally they don't delegate control over ip addresses to leased servers), and a DKIM or SPF policy (which I believe is default on most modern DNS configurations).
There is a vast array of items that could be going wrong, you could be blacklisted (Blacklist Check), you may not be using a SPF or DKIM key on your DNS, or users could have reported your address as spam (like the above example message), or you may not have a reverse DNS entry for your server IP address (which would get your domain blacklisted through some overzealous services).
Also, if you're sending mail from one domain (email@example.com) on behalf of another domain (firstname.lastname@example.org) gmail also may be dropping the messages as well for "masquerading" as another entity.