This is Finley from the Social Care team at Shopify. Thanks for your question.
I can definitely understand that you don't want to see the order count for orders that no longer require your attention.
Because the number you see next to the Orders tab includes all orders that have yet to be archived, can you please confirm for me if you archived your orders like so:
1) Archiving the order individually
You can archive individual orders by clicking the order, clicking More actions, and then Archive:
2) Archiving the order in bulk
You can archive orders in bulk from the Order tab by selecting multiple orders, then clicking More actions, and then Archive orders:
Another point to note, in case you don't already have this setup is that you can go to your Shopify admin > Settings > Checkout > Order processing section and enable automatic order archiving. This will mean that any orders that are marked as Paid and Fulfilled will be automatically archived and removed from the Order tab's count.
Let me know how you're doing with this and if you were able to have this resolved! I'm happy to take a closer look if you're still having any issues there.
I hope you have a great day!
Thanks for letting me know, @Newcomer2020.
I'm happy to hear it's been resolved! A celebration dance is certainly in order haha.
If you have any other questions, please feel free to reach out to us.
All the best, Eleanor!