how does the poetry try to overcome her fears at the time of parting from her mother ?

The last line of poem states that "but all I said was,see you soon Amma,all I did was smile and smile and smile...."
This shows that there is less hope that Kamala Das will meet her mother next time but her mother must not come to know about her childhood fear she hides it by smiling.
So smile is the the only way she tried to overcome her fear at the time of parting.