Why does thyroid hormone cause exophthalmos?

Exophthalmos. It does not. Graves disease which is associated with prominent eyes causes antibodies to inflame the surrounding tissues around the eyes. Graves also causes antibodies to stimulate the thyroid causing hyperthyroidism. It is not the high thyroid hormone levels that cause eye prominence.
It doesn't. Thyroid hormones at normal levels do not cause exophthalmos. Increased swelling of the orbit and surrounding muscles can be a consequence of grave's disease, which causes metabolic changes leading to the swelling and exophthalmos. The precise cause of exophthalmos in grave's disease is not clear.
It doesn't. Graves' disease can cause both high thyroid hormone levels (hyperthyroidism) and bulging eyes (exophthalmos). The cause of both of these manifestations is antibodies that target a person's own proteins. So it's not really correct to say that the high thyroid levels cause the eye problems. While they do both occurs in graves' disease, other causes of hyperthyroidism do not cause the eye problems.