A carrier pigeon brings a letter. In the sentence ”鸽子的腿上多了一封信”, I do not understand the use of 多了, unless it is used here as a verb meaning "to have", as in "the carrier pigeon had on it's leg a letter". However, I haven't found any grammar or discussion about 多 or 多了 that points to it being used with such meaning.
To translate 多了 literally would be confusing as it literally means "an extra or more of something", since there is only one letter attached to the pigeon's leg not an "extra" letter.
I would translate 多了 in the context of the sentence as "appears to have", i.e. "On the pigeon's leg it appears to have a letter"
Because the word 多 in this sense does not mean "many / a lot / extra" but to carry the idea that "there was nothing before, but there is something now"; as Alan Zzz puts it, (from 0 to 1)
Thus, we can say, "With a quick wave the magician's hand 多了 a rabbit"
多 = more, much, extra
多了一封信 = to have an extra letter
There is an extra person in our group.
In this case, the sentence can be translated to:
There is an extra letter on the carrier pigeon's leg.
Note: This sentence doesn't make sense as a single sentence. The pigeon has to be mentioned somewhere in the previous text.
If the pigeon's leg already has letters, 多了一封信 would mean 'has an extra letter'
If the pigeon's leg didn't have anything before, 多了一封信 would mean 'there is a letter (that wasn't there before)'
If a room was occupied, 房中多了一人 would mean 'there is an extra person in the room'
If a room was unoccupied, 房中多了一人 would mean 'There is a person in the room (that was unoccupied before)
We could omit the words in brackets in English if the reader can presume the pigeon's leg had nothing before and the room was unoccupied from the context
But the pigeon is back! And there is a letter on its leg
But the pigeon is back! And its leg has a letter on it
the reader can presume the pigeon's leg has nothing before, so we don't need to mention it