I imagine these days one could send a Subject Access Request to ask for whatever data AirBnB hold on you. Assuming there's some digital record of an internal conversation, or mark/comment on your record, you'd be able to obtain it.
I doubt they would provide you with any internal communications they have on you. After all, they can just claim they no longer hold any info except what they already told you (that you are banned) and you have pretty much no recourse.