Read this passage from the beginning of the story. "I thought she would never know!" Mrs. Li said.
"I just said yes so that I could take the baby and go."
I made a soft coughing noise and placed the tray on the table.
"Mrs. Li," I said as I bowed low. "Teacher is here."
She snorted with irritation and waved her arms, her voluminous silk sleeve flapping like a flag of surrender.
"Go," she dismissed me. I hid my smile and tried to walk humbly, as all the browbeaten servants were supposed to do.
Why does Lingsi hide a smile as she walks away from Mrs. Li?

She doesn't want to reveal that she knows her mother had gotten the better of Mrs. Li.

Shes trying not to laugh at Mrs. Li's waving arms

She knows that Mrs. Li does not like the servants to smile or show emotion in front of guests.

She wants to appear obedient and browbeaten like the other servants