How to resolve grading dispute between TA and Lecturer?
The nature of the dispute makes this problem difficult.

As a mathematics (BS) and computer science (MS, PhD) student I have done numerous exercises that required proof of the existence of a natural number N such that for all n>N some inequality is true. In addition to limits in mathematics, they show up in computational complexity analysis of algorithms.

Every time I have done one of those exercises I have picked a value of N that made the proof as simple and clear as I could. Often, I was aware of a smaller value of N that would have required a longer proof. I have never been marked down for picking an unnecessarily large value of N.

Any finite value N, no matter how large, such that the inequality is provably true for all n>N is equally good. That is an important aspect of these definitions, something the students should understand and apply.

If smallness of N were going to be a grading factor, despite its irrelevance, it should have been announced in advance.

That said, it would have been better for the OP to discuss the matter privately with the professor, and perhaps with more senior professors. The OP should not encourage protests directly, but should state the professor's decision and recommend that follow-ups be forwarded directly to the professor or offer to forward them on the students' behalf.