What does “on top” mean?
"On top" here refers to the top of the box, "of the box" has been omitted while speaking. You can understand "with a faux Asian "thank you" on top" to mean "with a faux Asian "thank you" on top of the box." When "on top" is used a sentence without an object following, it is usually related to the object that has been mentioned previously in the sentence. Ex: I baked a strawberry cake and wrote "Happy Birthday" on top [of the cake]. Ex: I baked a pizza and put extra cheese on top [of the pizza].