Is garcinia cambogia bad if I have no thyroid gland?

It's important to realise that Garcinia cambogia is classified as a dietary supplement in the United States which means that it is regulated as a food product and has not been subjected to the same safety or efficacy requirements as medicines. As such there is no literature supporting its safety in patients with thyroid disease.

Garcinia cambogia is an extract obtained from the dried fruit of the Garcinia cambogia tree, also known as Brindleberry or Malabar Tamarind. It has long been used in traditional South Asian dishes, including curries and chutneys. Many also use the fruit for curing fish and preservation. The plant is also added as a spice on meals to make them more “filling” and help with the management of appetite.
The skin, or rind of Garcinia cambogia fruit contains large amounts of hydroxycitric acid (HCA). HCA is thought to promote weight loss but experts are unclear as to how HCA works or if it really does.

For more information see: https://www.drugs.com/garcinia-cambogia.html