This law was intended to decimate the fast growing Chinese-American population of that time period by prohibiting unmarried Chinese-American men (railroad workers, etc.) from returning to China to marry Chinese women. Segregation laws also prohibited Chinese-Americans from marrying non-Chinese. The exclusion was mostly effective and the Chinese-American population decreased until the exclusion was repealed more than 60 years later.
Since all of people directly affected by the exclusion law are likely deceased, an apology at this time would be entirely for educational purposes. Should we be teaching our children about white supremacy in our country's history? Or is that something best forgotten about?