Which term could describe an expression of annoyance?

The term that best describes an expression of annoyance is "countenance." In this context, "countenance" refers to a person's facial expression or demeanor, which can indeed convey feelings such as annoyance. When someone is annoyed, their facial expression may reflect this emotion, making "countenance" an appropriate choice.

The other options do not appropriately capture the essence of annoyance in expression. "Gratuitous" typically means something unnecessary or unwarranted, which does not relate to facial expressions or emotions. "Dubious" refers to something that is doubtful or questionable, and while it can imply skepticism, it does not directly convey annoyance. "Rudiment," on the other hand, denotes a basic principle or element of a subject, which similarly has no direct correlation to an expression of annoyance. These distinctions underscore why "countenance" is the most suitable choice in this context.