The sauce tasted weak, so she added onions and spices to give it

zest
virtue
purity
luster

The sauce tasted weak, so she added onions and spices to give it zest.

To enhance the flavor of the sauce, she added onions and spices. This not only adds zest to the sauce but also brings out its natural flavors. The onions provide a savory and slightly sweet taste, while the spices add depth and complexity to the overall flavor profile of the sauce. By incorporating these ingredients, the sauce gains a more vibrant and robust taste, which helps to elevate its overall quality and appeal.

In this case, the word that best describes what the woman added to the sauce to enhance its flavor is "zest".

To arrive at this answer, we can eliminate the other options by understanding their meanings:

- "Virtue" does not fit in this context because it refers to moral excellence or righteousness, which does not relate to taste or flavor.
- "Purity" also does not fit here as it refers to the state of being free from contamination or pollutants, which does not describe enhancing a sauce's flavor.
- "Luster" refers to brightness, shine, or radiance, which is not applicable to taste.

Therefore, "zest" is the most appropriate word as it means adding a quality or flavor that gives something a more interesting or enjoyable quality. In this case, it refers to the woman adding onions and spices to make the sauce more flavorful and exciting.