I purchased a puppy from a private breeder. All puppies and parents were extremely well taken care of. unfortunately, we only had the puppy for 2 months because my son's allergies. I placed an ad on a website looking for a home for the puppy. We sold the puppy. There was no contract and no health guarantee as also with the breeder from where I got him from and with the new family. now the family has notified us that after a visit to the vet for small leg injury, he was diagnosed with demodex mange. the vet stated it is an inherited trait from the parents and thus recommended for him to be neutered and not bred, so the family is somewhat upset. they are requesting the return of their money and that I should contact the breeder where I purchased him from.
Can anyone advice on what I should do?

It was their duty to check out before purchasing. They got a deal, it had not been picked up on before, which you can show from where you had taken it to the vet.

I would recommend speaking to a board certified attorney in your area, maybe see if they offer a free consultation, and then see what your states laws are for puppies. I know in my state, FL, when you purchase the puppy it legally has to come with a certificate of good health that is dated no more than 10 days later from the time you purchase your puppy.