Yes, you can delete a duplicated payment in your register. To properly manage your books, you will need to unreconcile transactions in that register up to the date of the duplicated payment. Delete one of the two payments and then reconcile that register again.
If you use merchant services, keep the payment labeled RECON within the Reference # field and delete the manual payment.
Modifying reconciled transactions will affect any reconciliations done after that change, so you may need to put in some work in getting your books caught up.