If it was me (I am not an analyst or otherwise held a roll where I was checking accountability in any way)...
I would write back per email (so I have written down proof and file it offline) asking for a basic explanation of why this is set up the way it is, as to you it is confusing and could be interpreted as your company taking advantage of their client's lack of oversight on their account. You welcome the manager(s) setting you straight, so you can explain things yourself if this subject/specifics ever come up again. It could be a verbal agreement that X amount of work (approved by C at the client company) is billed out additionally, or they get billed that extra amount annually if they exceed Y hours of billable time... and no one ever updated the accounts on your end to reflect this addendum because it's just gone on forever. But it should be explained and then added to the internal record you mentioned you should do in option 3 - not just "we're billing them extra" but WHY they are billing them extra.
You know how best to phrase things to your immediate boss, so put it in friendly language and just explain that you're worried because your first reaction was something looks shady here, and you know it couldn't possibly be that... and you need it explained completely so you can add the explanation to the notes section of the account so no one in future auditing will miss that this is completely okay and approved by client company.
You'll either get the brush-off (shady business practices confirmed), or they'll explain that this is above board because of reasons, and either way, you're okay yourself.
So basically play dumb and ask for them to help you understand, and if there isn't a satisfactory explanation, then move forward based on your own moral compass and how much that plays a factor in your job satisfaction at that time.