I normally think of lost property as being found in a public place (see Devorim 22 (2) “you shall bring it into your house”).
If it is already in a person's house as with a wrongly delivered letter (by the mail service or by hand) , in what way do the laws of returning lost property change?
I might have thought he has lost the ability to ignore the item ((Rashi on 22 (1)) if for example he is an honored sage, and it it is beneath his dignity to lead animals or carry packages in public places).
According to this article (Q 33) you would need to return it. It makes no difference if it was delivered by mail or hand-delivered:
If mail was mistakenly delivered to you, you should give it to the addressee or return it to the sender.
This comment does not appear to be sourced within the article and is mentioned with regards to gifts sent in the mail. There he cites other sources from Chosehn Mishpat and Tzitz Eliezer. I don't have access to these sources, now, to see if they address this issue.
There are two other aspects as to why it seems that you may need to return the letter. First, the letter clearly has a siman as it is addressed to someone specific, and we can assume that if the owner had it, he would take care of it and guard it and would be concerned for its loss... for most items. (Personally, if you got my electric bill and were willing to pay it, I'd say you can keep my bill ;- Same goes for junk mail.)
The other aspect may relate to din demalchuta din. In U.S., it is illegal to open someone else's mail. This is mentioned in that article. Thus, it seems that you have to return the item, and, I assume putting it back in the mail box, or better, bringing it to the post office, would do the trick.
Lost & Found # 4
Q: If the government requires turning in lost items to police regardless of the owner or circumstances of the lost item, is that also a halachic requirement?
A: There is a halachic principle that dina d’malchusa dina, the law of the land has validity. However, there is significant discussion among the authorities about when this rule applies (C.M. 369:6-10).
Regarding treasures lost at sea, which one is permitted to keep, the Rema writes that if the king or beis din instituted that they must be returned, one must do so. The Rema writes a similar rule regarding returning a stolen item, even after the owner abandoned hope of reclaiming it (C.M. 259:7; 356:7).
This seemingly indicates that the rule of dina d’malchusa applies also to hashavas aveidah. However, some Acharonim write that between individuals, dina d’malchusa applies only when there is also an institution of beis din to this effect; then the law becomes common practice. Or it applies between individuals where there is an ethical recommendation (lifnim mishuras hadin) to return the lost item. Where there is absolutely no halachic basis to return an item, the rule of dina d’malchusa does not apply (see Shach 356:10; Ketzos 259:3).
