Hello. That wasnt the reason for his ban, you can ask him exactly what the reason on the ban says.

Hello! ηιgнт ƒυяу®,"slobbyknobby" said that the ban reason was that he was using offensive language. 

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So, what should be done to unban him? Will it help if he wrote an apology email to Mech Arena team? Could you please help me with the legal procedures that should be done?

If that's not the reason you banned me why did you also delete my posts?

The posts with offensive language were deleted.

What was it that was "offensive" about the language in my posts?

I think that was already explained to you in the ModMail on Discord - which you even admitted you used offensive language. So I'd end my part here.