"I saw the girl, who is standing outside our house"

One time you put a comma after "girl", making the relative clause appositive, and one time you didn't use a comma, making the relative clause restrictive. That's confusing. Which is it? Let's consider both possibilities:

a) I saw the girl who is standing outside our house.
b) I saw the girl who was standing outside our house.
c) I saw the girl, who is standing outside our house.
d) I saw the girl, who was standing outside our house.

I think they are all okay, but all mean different things. Since restrictive clauses have information about prior context, while appositive clauses add information not part of the context, we can approximate the meanings this way:

a') A girl is standing outside our house, and I saw the girl.
b') A girl was standing outside our house, and I saw the girl.
c') I saw the girl, and the girl is standing outside our house.
d') I saw the girl, and the girl was standing outside our house.

If we add the information in the question that the girl in question is known to have been standing outside the house previously and is still there, that would make the a) and b) versions equivalent, since the "is" and "was" versions work equally well to identify the person meant. If it is possible that the girl who was standing outside the house and the girl who is there now are different individuals, these are no longer the same.

In a comment above, Peter Shor seems to allude to a rule of older English that forces a mechanical agreement of tenses in older English, which would imply that the "was" of the relative clause could have the sense of a present "is". I don't know about that, but it makes things more interesting.