To remove notifications from the Notification Center simply set your icon badge number to zero.
[[UIApplication sharedApplication] setApplicationIconBadgeNumber:0];
This only works if the number changes, so if your app doesn't use the badge number you have to first set, then reset it.
[[UIApplication sharedApplication] setApplicationIconBadgeNumber:1];
[[UIApplication sharedApplication] setApplicationIconBadgeNumber:0];
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