**Core Concept**
The process of post-transcriptional modification of mRNA involves the addition of a 5' cap and a poly-A tail to the messenger RNA molecule. This modification is crucial for the stability and translation of mRNA in eukaryotic cells.

**Why the Correct Answer is Right**
The modification of mRNA involves the enzyme **guanylyl transferase**, which adds a 5' cap to the mRNA molecule. This 5' cap is essential for the recognition and binding of mRNA to ribosomes during translation. Additionally, the enzyme **poly-A polymerase** adds a poly-A tail to the 3' end of the mRNA molecule, which is also crucial for mRNA stability and translation.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect as it does not directly involve in the processing of post-transcriptional modification of mRNA.
**Option B:** This option is incorrect as it is a type of RNA polymerase involved in transcription, not post-transcriptional modification.
**Option C:** This option is incorrect as it is a type of enzyme involved in protein degradation, not mRNA modification.

**Clinical Pearl / High-Yield Fact**
The 5' cap and poly-A tail are essential for the stability and translation of mRNA in eukaryotic cells. The absence of these modifications can lead to mRNA degradation and reduced protein synthesis.

**Correct Answer:** C. Poly-A polymerase.