Hmm...
Mentioned before, but there are two possible kinds of transporters in science fiction.
1. Distorters. These devices force two separate 'places' to be congruent in space time. You walk from one space to another without having to travel between them, because space/time has been distorted to make those places adjacent. This 'transporters' don't kill you.
2. Everything else. You are disassembled, stored, transmitted, and reassembled somewhere else. You die, and duplicates happen. (No confirmation of receipt at the other end, so you're re-created at the beginning.)
I'm pretty sure that Larry Niven had both kinds.
The puppeteers had 'stepping discs' which were distorter technology. This is because they were unwilling to die using regular transporters.
Humans used transporters, which used the disassemble/reassemble method.
There was one pair of transporters found that cleaned out all the detritus of long life, resulting in, effectively, a perpetual youth machine.
In that, one of the booths had a cloud of settling dust, that was supposed to be everything that wasn't required in the, now, healthier person.
Somehow the products of aging are transported without affecting the user in the booth, here is the scene:
The lights were still on in the vault. Indicator lights glowed on the console. With luck the booths would work too. He stepped into one and looked for the dial.
No dial, just a button set in a slender post. No choice about where he was going. Corbell wondered if the Norn would be waiting at the other end. He made himself push the button anyway.
Nothing happened.
He cursed luridly, pushed out of the booth and tried the other. The second booth didn’t even have a door, and there was fine dust floating in it. What the hell?
(Larry Niven - A World out of time)
It takes Corbell a while to understand that he is now younger. (His white hair grows out, IIRC)
No explanation of how the booth could remove stuff from the body without doing damage.
If I'd written the scene, I'd have him appear in the second booth, and see the dust falling in the first booth. (Both booths are in the same room).
(That would have indicated that stuff was discarded during the disassemble stage.)