Objection is available for the flawless sentences that seem to have been rejected without a clear reason and is only available for the rejected sentences among others that have been completely proofread.
However, objection can only be accepted if the sentence is completely flawless, meaning that your request may be rejected in other cases.
You can click the participation history from the Arcade start page and change the "all" filter to "Fail" in order to see the objection icon for each sentence.
In addition, since Flitto's guide to the conversation section clearly mentions Flitto's own rule about not being able to change the results that have been decided based on several users, it is not possible to raise an objection for the sentences submitted in this section.