The correct answer is C. tact.
Tact is the ability to deal with people in a sensitive and considerate way, especially in difficult or delicate situations. It is the ability to say or do the right thing at the right time, without causing offense or embarrassment.
In the given question, the issue was of the highest sensitivity and required the greatest finesse and delicacy. However, it was handled in the most slapdash manner, which means in a careless and negligent way. This shows a lack of tact on the part of the person who handled the issue.
The other options are not as relevant to the given question. Carefulness is the quality of being careful and attentive to detail. Attention is the act of paying close attention to something. Action is the act of doing something. While all of these qualities are important, they are not as important as tact in the given situation.
In conclusion, the correct answer is C. tact.