**Core Concept**
The acid-fastness of tubercle bacilli is a characteristic feature of Mycobacterium tuberculosis, which allows it to resist decolorization with acid-alcohol during staining procedures. This property is due to the presence of a unique cell wall component.

**Why the Correct Answer is Right**
The acid-fastness of tubercle bacilli is primarily attributed to the presence of mycolic acids, which are long-chain fatty acids covalently linked to arabinogalactan in the cell wall. Mycolic acids are resistant to acid-alcohol decolorization, allowing the bacteria to retain the stain and appear acid-fast. This unique cell wall component is a key virulence factor of M. tuberculosis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the cell wall of M. tuberculosis does not contain a significant amount of teichoic acids, which are found in the cell walls of Gram-positive bacteria and are not responsible for acid-fastness.
**Option B:** This option is incorrect because the presence of a capsule is not directly related to acid-fastness, although the capsule may contribute to the virulence of M. tuberculosis.
**Option C:** This option is incorrect because the presence of a unique cell wall peptidoglycan layer is not responsible for acid-fastness, as peptidoglycan is a component of the cell walls of many bacteria.

**Clinical Pearl / High-Yield Fact**
Mycobacteria, including M. tuberculosis, have a unique cell wall that contains mycolic acids, which are responsible for their acid-fastness. This characteristic is used to distinguish mycobacteria from other bacteria during staining procedures.

**Correct Answer: C. The presence of mycolic acids in the cell wall.**