Issues with emails coming from Zendesk

Issues with emails coming from Zendesk

We use Zoho Desk and many times when customers have their own Zendesk account they will loop our support email address into their Zendesk tickets. Zendesk uses a unique email address for every ticket by including the ticket # in the email address. This causes several different issues in Zoho Desk:
  1. It will often create a new ticket for every reply they make
  2. It spams our contact list and creates a new contact for every ticket
  3. The systems will bounce back and forth notifying each other that a new ticket was created or commented on over and over.
Is there anything that can be done to prevent these issues? Zoho Desk is sometime good about merging duplicate tickets, but it's not perfect. The bigger issues are our tickets and contact lists getting filled with junk. Here's just one example of many: