I think it is related to the application preferences file which is located at ~/library/preferences or /library/preferences folders, depending on your application installation. If the app is installed to be used by current logged in user, the .plist file is located at ~/library/preferences, and otherwise it is placed at /libaray/preferences.
When you remove an app from Applications folder, it's related files, such as preferences files, application support files, and cache files are not removed, as they are placed some where else on the system. To completely remove an app, you should search your system for the application specific file name, and include system folders in the search options. You will see there are other files out there which are associated with the app. Remove all of the completely.
In this special case, since you just want to remove the badge file, I think removing the .plist file is enough. If you remove the .plist file and don't get the desired result, remove other application associated files.
The .plist files, are where your application store special settings, usually user preferences.
Hope that hellps
Mani Ghasemnia Hamedani