Do the antibodies in a patient suffering from Hashimoto's, attack the thyroid hormones or the thyroid gland (or both?)?
Hashimoto's Thyroiditis is an autoimmune disorder where autoreactive attack on the actual thyroid tissue results in hypothyroidism. Pyzik et al., 2015, provides a good review of what we know about HT. The prevailing theory is that nonspecific infection can induce HLA expression on thyroid cells through the action of interferon gamma. 

HLA is an antigen-presenting complex in humans that in our case is the major histocompatibility complex II or MHC-II you will see in texts (to avoid confusing names). Processed segments of protein are loaded onto the MHC-II, and displayed to the extracellular space where T cells positive for CD4 can recognize them. CD4+ T cells, upon recognition of MHC-II, are stimulated into T-helper or Th cells that are specific for the protein antigen they found on the MHC-II. The problem with MHC-II expressed by thyrocytes and the like is they can load either foreign or self peptides, so if it loads a part of thyroglobulin (Tg) on there and that's what the T cell recognizes, it's going to produce an immune response specific for Tg in a complex series of downstream events.

Being said, supplementation of thyroid hormone is a good treatment for hypothyroidism but it won't stop the attack on the actual gland. Thyroid hormones aren't often attacked by autoimmunity because they aren't protein antigens, and different subsets of cells respond to non-peptide antigens.