My first thought was that you might have been receiving a joint pension, but that can't be the case as they sent you £500 separately.
As others have said, it is meant to be £500 per household. If 2 of you claim separate State Pensions you are paid £250 each.
You do need to get this sorted, as they will ask you to repay overpayment. I see they haven't asked for last year's, but once they realise, they will!
As you feel wary, I suggest that you either follow Pammie's advice and send a tracked letter, or:
I would ask at the local Library if there is an advice service such as CAB or other local service to help you in your contacts with DWP. Take all of your State Pension paperwork and ask their advice. In some circumstances they will phone DWP for you. They will also help you to draw up a letter if that is best.
You also need this sorting properly as it may affect other benefits or taxes.