I think when Ian said that he wanted to get something from the apartment it could be that box but also the envelope that was under it maybe? I think I saw something that looked like letters but who knows.
When he went into hiding, he left behind what was precious to him and wanted a so called 'clean cut' from everything.
Yeah it can be interpret both way ;(( but there is no 100% indication that the box was what he came for and also the part where one of the gang members saying something about Jason along the line " his prodigy left him.." (if I'm remembering it correctly) just makes me think that there is more to it but who know. ┗( T﹏T )┛
My first thought before this chapter is that he left something of his own past behind... about his mom, his drug abuse problem or like you said something about Jason or the gun he used to kill the golfplayer... or something Jo gave him so if Jo went back to the apartment and found it, he will know its over between them.
But it would make sense if it was the earrings and chain because until a few chapters ago, Ian still believed that TJ could run away from everything to be with him... it's something that is special to him that he would risk his life and Ian's pretty chained to his past with TJ
For me that necklace and earrings are important in a way that's what he wear in the past, and ian love that kind of accessories so idk why people tied this with tj when tj is the one copying his style lol. But like if it's really to take only that, then I question doyak's writing if it's not something related for his escape plan or for his safety.
It's also don't make sense to tied it with tj when Joseph wanted to inform about tj and Ian immediately brushed him off and to not talk about that guy.
If it's not something relate for his safety or related to something that benefits him then the writing would be underwhelming and I would be surprised if doyak write something that's anti climatic

Just wanted to clear something up because I just read the raw and you guys might have seen panel of a cigarette box containing the matching necklace and earring that Ian has with TJ and seeing on twt saying Ian come back for that. NO. It's not really like that. The cop that was in season 1 who is in cahoots with TJ was searching Ian house. Which he open those cabinets and saw the box of cigarettes and under there was envelope. He empty the box of cig and find the earring and necklace but was immediately interrupted by another cop so he left that cabinet alone. And do correct me if I'm wrong but wasn't there a panel of someone saying something along the line "now that Jason's prodigy leaving him..." And Ian was the one who left the gang. I don't think he came back for the box. Yes the jewelry hold emotional significant but with the way he is acting I don't think that what he wanted to get.
Twt is not that of a reliable source because they tends to distort things into their own narrative and also because it's just panels that we are getting . We don't have the whole context. So do wait for the raws to drop of this chapter to drop here and hopefully y'all don't jump to conclusions and hate on Ian