There is currently no functionality to remove a product from sale on Catch within the Neto back end. So doing this needs to be done directly within Catch and seperately unticked for Catch within Neto, which is a poor workflow.
Logically I would have thought that "Approved to show on Catch" would be flag that either allows or disallows a product to be sold on Catch. This is not the case. If it is unticked and there is stick stock on Catch, it simply removes the sync but leaves the stock there, so stock quantity never updates.
From my testing this appears to be the case even if a product is marked inactive. Inactive products should not be shown anywhere. But if a product is inactive and 0 on Catch and then gets updated with stock (such as automatically via a data feed) it will then update the stock on Catch and be able to be sold. This is the opposite of the functionality of the eBay Marketplace, where you can set eBay to end listings for inactive products automatically, and it's not possible to create a new listing on eBay if it's inactive.