ZTO express staff asked me to write down the claim for no damage in the remarks column of the express bill? Is it reasonable?

In fact, it is unreasonable for the courier company to ask for this. But you are dealing with a courier who is afraid to accept the job. The courier company can't avoid collision during the consignment process, and the damage probability is high! However, as long as your internal packaging is intact, it will usually be fine.

If you are worried about late damage, you can contact the recipient before signing for it, unpack it in front of the courier and check it to make sure it is not damaged before signing for it. If it is damaged, please refuse to sign for it, and ask the recipient to contact you, and then contact Zhongtong customer service to let them explain and communicate the solution to you.

Even if you write the words "no claim for damage", it doesn't mean that the courier company can not be liable for the losses caused to its customers during the delivery process!