What is incumbent upon an illiterate woman who vowed a sum of money in exchange for reciting the Quran, and stipulated that the sum be distributed in the Prophet's Mosque instead of her own country?

Undertaking a vow is disliked (makrooh). However, if one vows an act of obedience to Allah, then fulfilling it becomes obligatory. Therefore, if the woman vowed to distribute the amount in the Prophet's Mosque to those who recite the Quran, she must fulfill it by sending it with a trustworthy person to distribute it as she intended.