Tenant threatening to break lease with mold excuse

[Kush Khandelwal]

My new tenants SFR in Grovetown, GA are complaining of possible mold and wishing to break the lease. Seeking any advice. To add more background.

I purchased this property in October - it's a 2004 SFR in great condition with no history of prior water damage. New tenants moved in 3 weeks ago in early December. They just wrote to me complaining of getting sick due to possible mold - while they cannot point to visible signs of mold, they claim they smell mildew and mold like odors which are making them sick.

I did a bit of digging and it doesn't appear that nobody in the past has gotten sick - this includes handymen and painters in the house, as well as the prior owners/residents. Seems that the new tenants may just be really sensitive to the air in the house. 

So now they've asked to conduct a thorough mold inspection, and if I do not agree, they want to break lease (without penalty) and leave. 

I understand that laws in Georgia regarding mold are unclear, so should I agree to the mold inspection conducted by them - where if there's mold then I should pay for remediation and fix? 

My fear is that they may not hire the most cost-effective and unbiased agency for the job. Also, I understand that the presence of mold doesn't always result in binary answers - given the humidity in GA there's always *some* mold in the air. 

Would love any advice on dealing with this issue!