If I'm understanding correctly, there was one letter sent to the previous owners of the home? I see three possible investigative avenues. Someone is either upset by the sale of the house itself, or by something about the previous or current owners.
More information about the first letter to the previous owners would be useful. Was it sent before or after they were planning to sell the house? If it was after they decided to sell the house, who would have known about their intention to do so at that time? Was the house on the market and who had shown an interest in it?
It seems least likely that the letters are being sent by someone with a longstanding ax to grind against the current owners, unless the letter was sent in a time period where the writer could have known they were moving to this particular house. Slightly less unlikely is ax grinding against the previous owners, but it's still possible that someone saw this as a perfect opportunity to disrupt their sale. Most likely, something about the transaction itself spurred the letters.
Practically, the only people who care who lives in any house are the neighbors. Neighbors can get very territorial and have private grievances so minor that no one else would ever be able to guess them. My money's on a neighbor. My second guess is someone who is aggravated by some financial aspect of the sale. Relatives involved in an inheritance dispute, current or former business partners or competitors, that kind of thing.
Edit: Another theory just came to mind, but it's rather off the wall. I feel bad even proposing this about the new family who I know nothing about, but a scorned mistress might also be bothered by the purchase of an expensive new home and could be upset enough to do something so "crazy." I'm imagining a scenario where the man promised to leave his wife for the mistress, but backed out. It could infuriate the mistress to see the wife get the upgraded life that she was expecting.
