Yes, it's perfectly polite. And seeing this person is a stranger, 'gift' is a more appropriate word than 'present'.
We tend to use the word 'present' for a more personal offering, usually between friends and family, on a particular occasion such as a birthday. A 'gift' is less personal. For example, a business can offer gifts to clients, or a magazine might give gifts to its readers, or a rich person might offer a work of art as a gift to an organisation.