Is the use of the word "been" necessary or proper when discussing a completed event?

Your example as presented is certainly grammatical and there is no need on grounds of grammar alone to remove been. It is a present perfect passive construction formed by the present tense of have + the past participle of be (been) + the past participle of the main verb (concluded). Conclude is used here with the general sense of bringing a transaction to an end.

Whether you omit been depends on the context and the meaning you’re trying to convey. The passive construction in this case doesn’t tell us explicitly who was responsible for the conclusion of the arbitration. It doesn’t say, for example ‘The arbitration between the claimant and the respondent has already been concluded by those concerned.’ However, it does perhaps leave us with the impression that the claimant and the respondent were involved in some way, even though an arbitration, by its nature, is normally conducted principally by a third party. If, on the other hand, you say ‘The arbitration between the claimant and the respondent has already concluded’ you are using conclude intransitively to mean ‘To come to a close or end; to close, end, finish, terminate’. In doing so, you are putting yourself at some distance from the action, and being even less committed to saying who was involved in the process.

Both are grammatical, so you really need to discuss with the other person what meaning and emphasis the sentence is intended to convey. Much will depend on the nature of the arbitration, who was involved in it, and how much you want to say about their involvement.

You can certainly write

The arbitration between the claimant and the respondent has already concluded.

No been. It's the difference between active and passive voice.

Conclude is an ergative verb: that is it, it may be used either transitively or intransitively, just like its synonym end:

The concert ended/concluded prematurely, because of rain. (intransitive)
Rain ended/concluded the concert prematurely. (transitive, active voice)
The concert was ended/concluded prematurely by rain. (transitive, passive voice)

Conclude is a little bit different in your context, however. An arbitration ends when the parties settle between themselves, or when the arbitrator renders a decision—which may also be called a judgment or a conclusion.

Your editor may therefore feel uncomfortable with your intransitive use, which implies that the hearing ‘ended itself’. Since you do not name the agent of the conclusion, your editor casts it impersonally in the passive.

It’s a very minor matter; it doesn’t really affect the meaning or, frankly, the stylistic impact. That’s what editors do; and it’s a small price to pay to get your paper published. Pick your battles.