What is the ruling on a man giving a gift to a woman to whom he is not related in any way, and without him having any ulterior motive or objective towards her?

If the gift is free of any unlawful purpose, then there is no objection to it. The Prophet, peace and blessings be upon him, accepted gifts from non-mahram (definition) women and gave gifts to some women. However, the intent of Islamic law behind exchanging gifts among Muslims is to increase affection. In this era, there is a concern that exchanging gifts between non-mahram men and women might open a door to evil due to weak religious commitment, and warding off evils takes precedence over achieving benefits. If it is highly probable that the gift could lead to falling into the unlawful, then it is prohibited.