It then occurred to me that I should take her myself and avoid all this proposed publicity. For if she were indeed an impostor it would save much unpleasantness for my family, and if she were the real Anastasia it was ghastly to think that nothing was being done for her....
The speaker's contemplation reflects a dilemma of personal responsibility versus public perception. They are faced with a choice between protecting their family and potentially neglecting the real Anastasia's needs.