Q. I have several network ovals labeled with subnets that don't belong. When I click on the network Info window I see a place where I can add and remove subnets, but I cannot remove one of these (incorrect) subnets, even though the lock is not checked.
A. These subnets come from one of two places:
added it manually, in which case you should be able to remove it, or
one of the devices attached to the network oval is reporting that it has an interface with that subnet. In this case, you can remove it, but it will be immediately added back.
If you don't think the subnet should exist at all, and you can't remove it, then you need to look at the links which lead to the network oval to see which links from which devices is reporting that subnet. (Bridges are one likely culprit.) You can then reconfigure the physical device not to report the incorrect network.
If you want the subnet to be in a different network oval, you can create a (new) network oval with the subnet and move/drag the links for that subnet to the new one. However, you may just end up with the situation where the new one now has both subnets, though the old one will have only one.
