How much weight does the tripos III carry for further PhD admissions?

I am planning on doing a tripos III this year in order to explore my interests and improve on a few bad grades in my undergraduate coursework. I would like to aim for a top 5 Math PhD program.

I have heard that the tripos exams are after most of the admission period in the US. Given this, how much of a factor does simply attending the tripos play in getting an offer for a PhD?