When the previous owners relinquished their dog to you they gave up any and all rights that they had period!

Giving a pup or dog away is not an open adoption.

After a dog is surrendered they have no rights for visitation or for deciding that they now would like to have the dog back. Once relinquished , surrendered and or having re-homed their pet they have absolutely no rights what-so-ever to the animal.

I would document and save any and all information regarding their communications with you as well as the times of each incidence of their coming to your home. I would also try and remember what they actually said as to why they were looking to re-home their dog when you initially spoke with them and when you decided to take the dog into your home.

They of course can take you to court, however by doing so they would only look foolish as no court would grant them what they are looking for. They can contract attorney’s if they wish but would be hard pressed to find one that would take the case as they have no grounds to stand on.

For your piece of mind, I would get a restraining order placed against all of the people sending messages and coming to your home. No sense in feeling uncomfortable within your own home.
Then if they continue you will have the documentation from court as well as all the information you saved about the harassment.

Have you taken the dog to the vet? (Should have been done immediately after taking the dog into your home) This would show that you have have ownership and are being responsible for his well being. Did the previous owners give you any paperwork on the dog? This would also be helpful but not all together necessary.

I am sure from the actions of these people that the dog is in a much better living situation.

As for the previous owners going overboard………. Yes Definitely ….. Just because they are remorseful for the decisions that they have made does not mean that they have any rights over the dog they did not want .. regardless of the reason.

Feeling bad for the children is one thing , but I would feel sorry for them for the environment that they are living in more so than losing their dog. It would be easier on the children to miss this dog and know it has a loving home rather than have given the dog back to them so that at some point they again decide they do not want him and re-home him yet again.

Enjoy your new dog, I am sure he is much better off and is quite happy being a part of your family.

Now forget about them and have a Merry Christmas (or what ever holiday your family celebrates) they will get over giving their dog away and more than likely are only doing so because of the kids and not for the best interest of the dog.

They do not have the right to demand their dog back and you shouldn’t feel pressured to do so especially seeing as there must have been a reason why they no longer own it and you do.

Edit: Just read the question you first posted, and yeah, you shouldn’t give the dog to them.
They seem unstable and making a dog go back and forth between homes can be very distruptive to its development