According to Terese Tse Bartholomew in Hidden Meanings in Chinese Art, Hong Kong, 2006, p. 192, the goose mates for life, and is therefore symbolic of weddings. It is also a harbinger of good news. This is derived from the story of Su Wu, who was captured by Xiongnu in the second century BC. He was able to inform the emperor of his whereabouts by attaching a letter to the leg of a goose that was returning to China, and he was subsequently rescued.
Compare a similarly constructed box carved as eight geese standing amidst prays of millet, dated to the 18th century and in the collection of the Victoria and Albert Museum, illustrated by M. Wilson, Chinese Jades, London, 2004, p. 57, no. 59.