Website spam/virus issues

Avg Bid (USD)
Project Budget (USD)
$30 - $250

Project Description:
On our cPanel server, we have a web hosting account that is facing a lot of issues.
They started receiving a lot of delivery failure notification of mails they never even sent.
This resulted in their legit e-mails now having a hard time being deliverable, for Microsoft/Google/Yahoo recipients many went to the junk folder.

We have tried setting up SPF, and to get a "clean slate" we created new e-mail accounts on their domain with another tld.
This worked well for a while, but now even the new e-mail accounts have bad delivery rate.
We are not sending out any newsletters, only responding to customers, etc.

The website accounts hosts some Wordpress sites, which maybe could be infected?
However we have not been seeing any strange or slowed down behavior of the website itself.

Are you able to help us investigate and SOLVE this problem?
Explain why/how.

Skills required:
Linux, System Admin, Web Hosting, Web Security, Wordpress
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