For AppMeasurement.js or s_code.js Analytics implementation, comment/remove Adobe Analytics script from website page to stop collection of Adobe Server call for a website. For Dynamic Tag Management(DTM), either deactivate the DTM Web Property or remove/comment the DTM embed code from each page of the website. There is no explicit setting that can stop collection of Adobe Server call. All the server call sent from a website are processed and billed according to the server call cost.
But if you don't worry about the Server Call, I would request you to create a Virtual Report Suite that can exclude the 'Old Apps' which will ease your reporting. Or if it is an Individual Report Suite, then you can hide the Report Suite which will not annoy you while reporting. But at any time, we cannot block the Server Calls at Adobe Side using Settings or Processing Rules.