**Core Concept**
The causative organism of syphilis is a spirochaete bacterium that belongs to the genus Treponema. This pathogen is transmitted through skin-to-skin contact, usually during sexual activity, and can lead to a range of clinical manifestations if left untreated.

**Why the Correct Answer is Right**
The correct answer is *Treponema pallidum*. This bacterium is a helical-shaped organism that is approximately 6-15 μm in length and 0.1-0.2 μm in width. It has a distinctive spiral shape and is capable of invading host cells, leading to the characteristic lesions and systemic complications associated with syphilis. The pathogenesis of syphilis involves the entry of T. pallidum into the bloodstream, where it can cause damage to various organs, including the skin, mucous membranes, and central nervous system.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because *Borrelia burgdorferi* is the causative agent of Lyme disease, not syphilis.
* **Option B:** This option is incorrect because *Bartonella henselae* is the causative agent of cat-scratch disease, not syphilis.
* **Option C:** This option is incorrect because *Haemophilus ducreyi* is the causative agent of chancroid, a different sexually transmitted infection.

**Clinical Pearl / High-Yield Fact**
It's essential to note that T. pallidum cannot be cultured in vitro, making diagnosis of syphilis reliant on clinical evaluation, serological tests, and sometimes direct visualization of the organism using darkfield microscopy.

**Correct Answer:** C. *Treponema pallidum*.