What is the meaning of the phrase "put up the back of"?
It was better to go to the curio shop. No one who saw her go in would think anything of it, and they were absolutely safe there. The owner of the shop knew who Charlie was and he was not such a fool as to PUT UP THE BACK OF the Assistant Colonial Secretary. What did anything matter really but that Charlie loved her?

from William Somerset Maugham
The Painted Veil

What shall I look for to find this phrase in a dictionary?

Question

What is the meaning of the phrase "put up the back of"?
It was better to go to the curio shop. No one who saw her go in would think anything of it, and they were absolutely safe there. The owner of the shop knew who Charlie was and he was not such a fool as to PUT UP THE BACK OF the Assistant Colonial Secretary. What did anything matter really but that Charlie loved her?

from William Somerset Maugham
The Painted Veil

What shall I look for to find this phrase in a dictionary?

Answer

In England we also use 'get someone's back up' e.g 'that comment really got her back up'

Answer

The phrase you need to search in a dictionary is, "to put someone's back up".

You'll see it means to make someone annoyed or angry.

Answer

It means "to make angry"