We have a Google Drive integrated app (marqueed.com) that allows you to authenticate and upload your Google Drive images from inside our app.
However, we don’t want Google Drive users to be able to open files (“Open with”) our Marqueed app from the Google Drive dashboard:

We don’t want our app to show up in the above screenshot, is there a way to do this?
Your application shows up in the Open With menu for those files whose MIME types or extensions are listed in the Drive SDK tab of the APIs Console: https://code.google.com/apis/console/
Just remove those values from both Default and Secondary MIME Types and Extensions and your application will not show up anymore.
For more details, check the documentation at https://developers.google.com/drive/register#setting_mime_types_and_extensions