Because it says "portatA" rather than "portatO", meaning that the l' is shortened from la (and not lo), I think.
If the shoes had taken HIM, the sentence would be:
"Quelle scarpe l'avrebbero portato alla fine della gara"
I am surprised that a verb which takes avere as an auxiliary must agree with the object -- I forget, is this a general rule? Or does it apply to only certain verbs? I remember that verbs that take essere must agree with the subject, but I don't remember when this one applies.
Well, I originally read it as speaking about the shoes throughout ( le avrebbero portato(e) was how I thought it should read. Upon rereading it, I discovered that the shoes were taking the female to the end of the race. I had misread it.
Little by little you will learn and it will sink in. Duolingo is one tool in the toolbox use it correctly and it'll do the job. There are other resources out there that will assist with enrichment. Use all the tools in the box to become a craftsmen