In English a goose could be either male (a gander) or female, as an individual of the goose species. Since we don't know the gender in English, "its" is most appropriate.
The man (Matthieu) has a clearer enunciation than the woman. Clear enunciation often includes the use of the French schwa which makes a final -e sound uh when the next word starts with a consonant sound. Also, French people living in the south-west tend to use the schwa and they speak more slowly. Typically, Parisians are said to "swallow" some syllables.
Je sais qu'il y a un autre mot pour "protect" mais "The goose protects its nest" devrait marcher aussi, n'est-ce pas?