What can be done, Islamically, regarding a girl whom the questioner wishes to marry, but her guardian has given his word to another person whom the girl does not desire?

If the maternal aunt informed her daughter of your intention to marry her, and the mature, sensible daughter agreed, and you are a suitable match for her, then you have a greater right to her, and it is not permissible for anyone else to propose to her. This is based on the Prophet's (peace be upon him) saying: "A man should not propose to a woman already engaged to his brother until the first suitor leaves her or gives him permission." There is a consensus on the prohibition of proposing after a clear acceptance from a legally responsible woman who is a suitable match, or from the guardian of a minor. However, if what happened was merely talk, devoid of agreement and the woman's inclination towards you, then there is no harm for others to propose to her. If the second suitor concludes the marriage contract, his marriage is valid, but he incurs sin if he knew of your engagement and the woman's inclination towards you.