Another interesting review linking gastritis and Hashimoto's Syndrome, indicating absorption problems can accompany Hashimoto's quite frequently and interfere with T4 uptake. The paper is downloadable in Frontiers in Endocrinology:
MINI REVIEW ARTICLE
Front. Endocrinol., 26 April 2017 | doi.org/10.3389/fendo.2017....
Hashimoto’s Thyroiditis and Autoimmune Gastritis
Miriam Cellini, Maria Giulia Santaguida, Camilla Virili, Silvia Capriello, Nunzia Brusca, Lucilla Gargano and Marco Centanni*