I'm going to leave BD for this night and so that you don't need to lose your night's sleep pondering this (
), I'll give you the right answer as you're so close anyway.
To Dori, Bilbo is something he dropped in Moria.
To Gollum, the Ring is something he dropped in Moria.
Legate can have the thread as he was the one to guess Gollum and to mention Moria (even though very vaguely).