if this bank issued bitcoin notes is accepted, they in effect can inflate it to a degree. as all the notes is not accounted for in the chain and thus it cannot be checked that it is correct in accordance to the chain. Aside from the issuer of the notes. And aslong as they keep the information about that to themselves, they can infalte it a little, and then a little, untill someone maybe finds out.
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Inflation can only be caused by an abundance of currency. Meaning, if there is less to go around, they will be worth more. The government can surely influence the currency, but not by much. I really should look deeper into this. But I don't think inflation will be a problem.
And about removing currency from the blockchain, they already can do it without notes.