I was once in a similar position although a far smaller amount, I contacted them said they should check their maths as they've paid too much. They replied saying no this is correct amount, I'm still not sure what was going on but they wouldn't take the money back. They're still a client but its not happened since.
I've also experienced a potential client say, are you sure? you should charge us more! They're also still a client, I didn't charge more but said just keep the work coming and well both be happy. I did increase my rates for new clients the next day.