I can't see that any real good can come from a challenge.
I went for a job some months back, quite a niche role that few are qualified for. It was an assessment day and all 6 candidates spent the day together. I was the only candidate with the experience and qualification to do the job, I had all the right industry contacts and knowledge, and as far as I could see, no-one else came close. It all went extremely well and I expected to land the job.
What I didn't know at the time (I found out afterwards from the retiring post holder) was that the successful candidate was a good social mate of the hiring manager and also his wife worked for the company. He had no industry experience or knowledge, something he was open about on the day, so it looks to be a case of pure nepotism. I had to press for feedback, when it came it simply said that another candidate was stronger. He wasn't even suited for the role at the basics level, let alone "stronger".
I was angry about that if I'm honest and I thought about challenging, but it's not like it would have (a) got me the job, (b) materially changed how that company recruits, and above all (c) done my reputation any good whatsoever. I got over it eventually and I feel I've come out of it with the greater dignity.
I've just accepted a far better post with a much larger company, with a 75% salary increase, so sometimes things happen for a reason. This job could well have tied you up for that next big thing... don't let it eat you up, be positive, and move on.