@LCunningham1 I’m glad @HFisher7 was able to help you find the view you’re looking for to manage the replies that need a response so they don’t get buried.
Since you’re in the 2nd month of using HubSpot for managing support, I thought I’d share a few helpful tips that I use to manage the inbox.
Add custom ticket properties to track relevant data for open convrsations and set them as the default at the top of the about record for tickets so they are visible from the right sidebar in the inbox.
Use emojis in the dropdowns for the properties so you can very quickly assess the situation at a glance - for example, you could have a property to track documentation status (especially if you’re using the knowledge base), it could be something like:
need new documentation
requires update, inaccurate or incomplete
documentation provided
Then you can create filtered views from Service > Tickets and even workflows that assign tasks to users related to the status of these properties.
I also recommend using emojis in your view names, it will make it a lot easier to pick the right one.
Another thing that’s helpful to differentiate new from old is to set an SLA (if you’re not already) - even if you aren’t holding your team accountable to the SLA, it creates a warning and past due notice that makes it very easy to differentiate what’s not been replied to yet:

Finally, I recommend coming up with a process for using Comments to flag what the next step is for any open items.
For example, if you’re waiting on a reply or approval for something, you could flag it with your initials and status:
JN - pending confirmation temporary fix was applied
the comments are nice because it adds a yellow highlight to your conversation:
and because you’ve flagged the thread after your last reply, you can very easily visually discern what threads have new replies from the customer.
I hope these help you make the most of the inbox and improve your team’s productivity, I love working in the inbox and am happy to help if you run into other questions!