Actually, a connector in a Logic App is a wrapper to an external system that uses a particular Azure resource (called the API connection). The API connection is an external resource with respect to the Logic App, but the Logic App is linked to it, because it needs it to call the external systems through the connector.
So, you can find the API connection resources in the resource group list of your Azure subscription, but in the Logic App blade, you will find an option to show all the API connections that are used by the Logic App:
Using this list, you can change the properties of every single connection that you are using in ...