If a couple, both carriers of an autosomal recessive disease (genotype Bb), wants a child without the disease, the required genotype of the egg must contain at least one B allele. Her first polar body will carry the B allele if the egg that is fertilized carries the B allele to potentially produce a healthy offspring.
The question at hand involves understanding how the inheritance of an autosomal recessive disease works and what statement would be true about a woman's polar bodies if she and her husband both are carriers with the genotype Bb. Since polar bodies are byproducts of oogenesis, which is egg formation, and we're assuming no crossing over, her polar bodies will contain the opposite alleles of whatever ends up in the egg itself. Therefore, her first polar body will either carry the B or b allele, depending on which one was separated into the oocyte that becomes the egg.
Given the scenario, if a child that does not have the disease is to be conceived, the egg that gets fertilized must carry the B allele to ensure the offspring has at least one dominant B allele and is not affected by the disease bb. Since the question asks about the polar body and we are looking for a scenario where a disease-free child is conceived, the correct answer is A. Her first polar body will carry the B allele if the egg needs to carry the B allele to avoid the disease.