She's furious and yes of course she accepts

Gretchen had seen Hakan push the nice young Kirghiz who had helped her throughout the lessons aside, subconsciously she knew that Hakan would not be an easy opponent, but her anger at the rowdy was immense, he had driven her close to the edge of white heat.

On the other hand, she realized that if she didn't act there would be a big brawl between Hakan's gang and that of the Kyrgyz, that wouldn't make her look good either. Under those circumstances she could as well accept the young Turk's challenge herself ...

Somehow like that, Ms. Fischer later rationalized the gut decision she made at that moment:

"Well then let's find out ..."

she said grimly and now totally focused on her opponent....