If malar bags are the result of a thyroid problem, then do they improve with the appropriate medication?

Individuals with Grave's disease can have swelling and malar changes associated with their orbital disease.  This generally to do not full resolve when the Grave's diseases burns out.  Grave's disease is associated with an overactive thyroid.  If you have been diagnosed as hypothyroid, a more common thyroid problem, this is generally not associated with a malar bag.  Most likely your malar bag is unrelated to your thyroid status. Generally these are addressed with fillers or lower eyelid surgery.  Consider consulting a fellowship trained oculoplastic surgeon.