The MobilePush SDK will control badging if the Inbox functionality is enabled in the configuration for the SDK.
If you do not need inbox, set "inbox":"false" in the configuration file and you'll be able to set the badge.
If you are using inbox, you can attempt to set the badge in a delayed fashion in your app's background notification hander. A short dispatch_after in your own handler for UIApplicationDidEnterBackgroundNotification (maybe 1 second) which would then call
setApplicationIconBadgeNumber for their own value.
This is untested but should be sufficient.