The correct answer is: C. the beginning of further concessions.
The phrase “the thin end of the wedge” means “the first of a series of concessions that will lead to more and more concessions.” In this case, the speaker is saying that if they give the other party this one concession, it will only lead to them asking for more concessions in the future.
Option A is incorrect because it is not necessarily a compromise on principles to give someone a concession. It could be a matter of pragmatism or simply being fair.
Option B is incorrect because it is not necessarily the least that could be done for someone to give them a concession. It could be a significant concession, or it could be a small concession that is still important to the other party.
Option D is incorrect because it is not necessarily inadequate for someone’s needs to give them a concession. It could be a perfectly adequate concession, or it could be a small concession that is still appreciated by the other party.