You can easily pause chasing for a customer group by following these steps:
Go to the Customers list.
Find any customer who belongs to the group you want to pause.
Click on the chain icon next to the customer's name. This opens the customer group.
At the top of the group page, click Chasing on/off to toggle chasing for the entire group.
Once paused, you can find customer groups that have been paused using the filter "Cust. Group chasing paused":
