The woman should be allowed to compete. To exclude her because of a trans history is a very obvious example of discrimination.
As for the argument about the effectiveness of sexual reassignment surgery. The truth is that being transgender is difficult and is more difficult for some than others. Most trans people are very much scarred by their upbringing. A lot of trans people will always look like their assigned gender no matter the surgeries and hormone regiments they are put on. A lot of trans people have zero support. It's no wonder that all trans people don't live happy, fulfilling lives.
But the procedures do work. They do eliminate/reduce gender dysphoria. What's needed to improve the lives of trans people is not to question their legitimacy, but to accept them as who they are.
And keep in mind surgery is a very small part of the transgender experience. Not all desire surgery and only 20% have had SRS.
Here's a study on the subject:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3043071/
Persons with transsexualism, after sex reassignment, have considerably higher risks for mortality, suicidal behaviour, and psychiatric morbidity than the general population. Our findings suggest that sex reassignment, although alleviating gender dysphoria, may not suffice as treatment for transsexualism, and should inspire improved psychiatric and somatic care after sex reassignment for this patient group.