Support

The concept of latest tickets is "any ticket whose status is Open". Open tickets are those where the last reply came from a client and demand attention from your support staff. The whole idea of having that page is to provide support staff with an overview of work that needs to be taken care of. Removing open tickets from that view is, therefore, inherently opposite to the intention of the page. You're asking me how to intentionally hide work you have to do. This will only result in a low quality of service.

If the last reply that came from a client indicates that you should not do anything until they post a new reply you can simply set the status to Pending. That's the intention of the Pending status: waiting for further response from the client.

If for any reason you want to put a ticket to the backburner you can always set up your own ticket statuses. For example, you can create a status "working on it". This lets you communicate to your client that you are on top of their issue and allows you to filter ticket lists (category pages) by it, letting you know which tickets are on the backburner.

Finally, if you have a bunch of tickets with a similar issue you want to track as a whole you can use the Ticket Buckets feature. You can put a bunch of tickets in a bucket and send out a reply to all of them (e.g. "We are working on this"). This sets the tickets on Pending status and they no longer appear on Latest Tickets. The bucket still appears in the bucket list, letting you track these common issues. You can remove the bucket once you have sufficiently resolved the common issue among all tickets.