I would think that (with some creative thinking) you should be able to get the piece out without having to remove the entire drain line. Is the piece still visible? If so, there are many things you could do to try and retieve it from the top. If not, what about compressed air (from the bottom) or a thin gauge wire (knotted at the end) to push it from below? If it's broken into pieces, how about using a shop-vac on the top to suck nylon twine from the bottom and then "floss" it out.
The ideas are endless....
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