TSH (Thyroid Stimulating Hormone) is a chemical released from the brain to increase T3 & T4 (Thyroid Hormones) when T3 &T4 levels start falling. Please post the exact T3, T4 & TSH readings.
If her T3 & T4 levels are on the lower side of normal range, TSH is levels are bound to increase. If she has no signs or symptoms of Thyroid disease she may be Euthyroid (Normal) or in sub-clinical thyroid disease.
Thyroid disease is many times more common in females than in males.
You may also have to get her Thyroid Antibody Levels checked to make a diagnosis.
She may have to avoid Goitrogens (Thyroid disease causing agents) in her diet like Cabbage, Cauliflower, Tapioca (Sabudana), and Peanuts.