I've had this in my drafts for quite a while but I don't think I'll expand on it soo... yeah.
Mako and Bolin find the Gaang's diary of recorded events and tips and gain inspiration from them. Also becomes their moral guide and makes them look forward to something in life. Until they find out the owners' actual names because the Gaang uses fake names in the book. Aka Toph's nicknames.
Or Sokka hands the book over to the brothers but they don't really recognise him so they keep the book with themselves.
A scene I envisioned under the cut
*Toph, Katara, Zuko are in the same place and Mako and Bolin are nervously shifting*
Zuko: What did you want to tell us privately and asked Avatar Korra to contact us for?
Mako: Well… years ago the two of us stumbled upon this book while we were on the streets and well… not exactly stumbled upon it but… more of the fact that someone gave it to us. They asked us to hand it over to their family but the book had no name and we didn’t exactly know who it was so...
Bolin: We read the book, which kind of turned out to be a diary? But it didn't really have any names so once again we didn't know who to give it to. So we just held onto it. It did help us in some way when we had to survive the streets so… yeah"
Katara: But why call us?
Mako: The book… there was a riddle in the end that we tried to figure out in hopes that it would lead us to the identity of the owner and well… Korra just waltzed into the room then and was like ‘that was Sokka’s book. More like the old team avatar’s travel book’ and now we knew who to hand it over to… we asked Korra to contact you. So… here you go. *hands over Katara a worn-out book
Katara: *misty eyes and lets out a gasp
Toph: What is it Katara?
Zuko: Unbelievable… It really is… Our diary Toph… our missing diary.
Toph: Snoozle’s diary? The one we etched our adventures on? *feels around the book* Still has the same dent there when Aang had thrown it in a fit.