打包 (dǎ bāo, literally, 'pack bag') is a well established tradition in China. Every restaurant from hole-in-the wall shacks to fine restaurants has this service. It is expected. The restaurants supply suitable containers.
I've also noticed that very little food is wasted in domestic kitchens. It is very such seen as a 'sin' to waste food. Famine is still a living memory. Wasting rice is particularly taboo.