You can delete just sub-channels.
I am using a Zenith DTT901, but the Insignia APT should be the same menu.
The channel edit feature will give you a list of all channels, including sub-channels.
Then move to highlight Channel Edit
Press select/enter to show the channel list. This will allow you to add/delete channels and create a favorites list.
On the left hand list, you will see all of your stored channels including sub-channels.
Highlight a channel or sub-channel and press enter/select to delete it. Then exit. The channel number is not really deleted from the list rather it is disabled. It can still be tuned if wanted. It remains on the list but greyed out.
Now the disabled channel will not be tuned when you use channel up/down, nor will it be shown in the simple guide.
The disabled channel number can still be tuned at anytime by inputing the channel number using the remote. It will also still show on the channel drop down list when inputing similar channel numbers with the remote. The channel can also be added (enabled) on the channel list in the same way it was disabled.