I just got a Chinese visa sticker in my passport. On the page opposite of the Chinese visa, there is a sticker that reads:
Attention
An expired US passport with a valid Chinese visa is good for travelling to China provided it is used together with a new US passport bearing the same name, sex, date of birth and nationality. If any changes are made to the above mentioned information on the new passport, a new visa shall be applied.
Can I remove this sticker?
Don't. At least not if you want to apply for another Chinese visa. I did it once, and the next time I applied for a visa, the Chinese visa authority rejected my application. The page where the visa was originally had a thin layer of glue. That alerted them, they checked, and indeed couldn't find a visa sticker for the visa they knew I had applied for. They told me they couldn't issue me a visa again until I either presented the missing visa sticker, or a new passport. I have two passports, so I gave them the other one, and got my visa.
Then in Macau, the Immigration officer saw this suspicious blank page, and again they refused to stamp me in. Suspicious, they said. So, again, being lucky to have two passports, I gave them the other one, and was let in.
After that I renewed that passport and never removed a visa sticker. Too much can go wrong.
Since I haven't gotten a good answer, and I have already been to China and back, I will share my experience for any one else with this question.
I don't know if you can remove the sticky note, but the immigration officers just stamped under it, so you should not worry about losing a page.