And sometimes the host will serve some dishes with his or her own chopsticks to guests to show his or her hospitality. This is a sign of politeness. The appropriate thing to do would be to eat the whatever-it-is and say how yummy it is. If you feel uncomfortable with this, you can just say a polite "thank you" and leave the food there. There are some other rules that are suggested you follow to make your stay in China happier, though you will be forgiven if you have no idea of what they are.
1. Never stick your chopsticks upright in the rice bowl, lay them on your dish instead. Otherwise, it is deemed extremely impolite to the host and seniors present. The reason for this is that when somebody dies, the shrine to them contains a bowl of sand or rice with two sticks of incense stuck upright in it. So if you stick your chopsticks in the rice bowl, it looks like the shrine and is equivalent to wishing death upon a person at the table.
2. Make sure the spout of the teapot is not facing anyone. It is impolite to set the teapot down where the spout is facing towards somebody. The spout should always be directed to where nobody is sitting, usually just outward from the table.
More at chinesefolkculture website.
