Bill Payment (Check) vs Manual Check Entry

Let me try to answer your questions with possibilities.

Bill payment checks are only created through Pay Bills or by matching checks in the bank feed. Once created, a bill payment marks that bill as paid and it cannot be paid again. 

Bank feed items can be matched or added but should not allow double posting to same bills.

Adding instead of matching is the #1 way in which duplicate entries appear.

First you need to verify that tgecregister does in fact contain double entries and that only one of each applies to each bill. You can review transaction history of a Bill to see exactly which payments are applied and then , with care, void or delete the check that is not applied to the bill.

Quite possible that the checks marked as bill payment were not created through the Pay Bills process but instead were simply created and labeled as such, thus allowing for duplication during the add instead of match process.