It doesn’t matter. The challenge is voted on by both chambers and the chance of the challenge being upheld by a vote is exactly zero.
I've been reading through these BC/COLB threads for months now, it took having another FReeper explain the difference between fact and truth re: the role of the Supreme Court, to assist in my understanding of why these cases are not being taken by the SC. As you note, even if Linder and a GOP Senator lodge an objection, said objection, challenge WILL be overridden by majority vote in both Houses. This one goes nowhere, regardless the important point of upholding the minimum in the Constitution.
Legislation to describe the procedure for qualifying candidates for federal office is necessary in order to keep this situation from becoming an issue in the future. Either Congress passes it, (Dem majority? Ho ho, don't make me laugh) or the states' legislatures do, but we are to the point that this must be done in order to keep the question from being raised again. It should have been accomplished when the question of Chester A. Arthur's qualifications was raised -- I had no idea that had occurred in the past, (nice omission by my American History/Government teachers) and if enough citizens had made a fuss back then in order to get the procedure set in stone, we would not be here with this today.