After you deleted the payment, you have to save the invoice without the payment.  Then you can delete it. 

I am not sure I understand this. The payment has been deleted but the invoice remains. There is no way to delete it. If I try to change the invoice to a zero amount, it gives the account a credit as though it has been paid, but there is not a record of payment any longer. 

After you deleted the payment, did you save the invoice without the payment?   Does it say unpaid?   If yes, you should be able to delete it.  If not, check with your program Admin.  They will have to give you security rights to delete the transaction. 

After deleting the payment, the invoice still says paid in full. 

Did you save the invoice and close the invoice.  Go out of that module and come back in. 

I have, its a issue I have been trying to figure out since Feb. 

Ok then run data verification.  File > Data Verification.  You will back up in the process.  Do not write over the original backup. This process can be helpful, it can also eat your data away and you may have to restore the backup.  

That did it. Thank you so much! I was not aware of the data verification. 

Glad I could help you!