Down Payment vs. Repayment

Hello r/personalfinance! I'm looking for some advice.

About two years ago, the military (U.S.) overpaid my wife about $12,000. We were aware of the overpayment and have kept it in savings until they would ask for it back. Well, that day has come.

Here is the twist... We are looking to buy a home within the next 6 months or so and would like to have a decent down payment. Here is my idea. The money is liquid. It's in our savings account. We can set up a repayment plan that is interest free and does not affect credit. I have enough income to cover these monthly repayments.

So this is my question to you guys. Use the $12,000 as a down payment as a pseudo interest free loan? Or just try to pay them back in one full lump sum?

Thanks for all of your time and advice!