**Core Concept**
The question requires knowledge of matrix bands used in dentistry, specifically for restoring Class-I cavities with lingual extensions. A matrix band is a crucial component in achieving a precise, symmetrical, and aesthetically pleasing restoration.

**Why the Correct Answer is Right**
The Barton band is a type of matrix band commonly used for restoring Class-I cavities with lingual extensions. It is designed to provide a precise, curved shape that follows the contours of the tooth, allowing for an ideal restoration. The Barton band is typically made of a flexible material that can be easily adapted to the individual tooth shape. This flexibility enables the dentist to achieve a precise fit, which is essential for a successful Class-I restoration.

**Why Each Wrong Option is Incorrect**
**Option A:** The Tofflemire matrix band is typically used for restoring Class-II cavities, not Class-I cavities with lingual extensions.
**Option B:** Ivory No.8 is a type of matrix band, but it is not specifically designed for Class-I cavities with lingual extensions, making it less suitable for this particular restoration.
**Option D:** The T band is a type of matrix band, but it is not the preferred choice for Class-I cavities with lingual extensions, as it may not provide the necessary precision and flexibility required for this type of restoration.

**Clinical Pearl / High-Yield Fact**
When choosing a matrix band for a Class-I restoration with lingual extension, consider the flexibility and adaptability of the band to ensure a precise fit. The Barton band is a popular choice due to its curved shape and flexibility, making it ideal for this type of restoration.

**Correct Answer Line**
✓ Correct Answer: C. Barton