In the condition of hypothyroidism the Thyroid Stimulating Hormone level is high in individuals. What signalling/metabolic pathway mediates this sensation of pain which is mostly experienced in feet and joints.
This isn't my field, and I'd love to see my answer surpassed by someone with expert knowledge. But I should say a recent case report (Pantazis, 2016), though it dealt with an unusual situation, discusses some of the current thinking:
hypothyroidism is characterized by decreased synthesis and degeneration of collagen. Hypothyroidism also inhibits epimerase, which results in reduced chondroitin sulfate and elevated hyaluronic acid, hence weakening the matrix. Moreover, it causes accumulation of glycosaminoglycans (GAGs) in the extracellular matrix (ECM), being involved in the pathogenesis of carpal tunnel syndrome during hypothyroidism and predisposing patients to tendon calcification
THs have known effects at the cellular level on the proliferation and differentiation of bone and cartilage. The hypothyroid state appears to induce abnormalities in these tissues, which results in such clinical manifestations as epiphyseal dysgenesis, aseptic necrosis, possibly crystal-induced arthritis, and an arthropathy characterized by highly viscous non-inflammatory joint effusions primarily affecting the knees, wrists, and hands. Neuropathic and myopathic symptoms accompanying hypothyroidism may manifest as joint region abnormalities when in fact there is no underlying arthropathy.
These paragraphs cite three much older sources. I don't see a tremendous amount of activity on this narrow issue in PubMed - the broader issue that this case illustrates is whether there are better ways of diagnosing and treating hypothyroidism to restore the balance more effectively; see Midgeley, 2019 for example.