Final answer:
TFIIS is the eukaryotic transcription factor that aids RNA polymerase II in the removal of incorrect nucleotides during mRNA synthesis, ensuring the accuracy of the transcription process in eukaryotes.
Step-by-step explanation:
The eukaryotic transcription factor required to aid RNA polymerase II in the removal of an incorrect nucleotide incorporated into the growing mRNA is TFIIS. This question relates to the role of various transcription factors involved in eukaryotic transcription, specifically those factors that are part of the class known as Transcription Factor II (TFII) and are responsible for the recruitment and functioning of RNA polymerase II during transcription initiation. Transcription errors may occur during mRNA synthesis, in which cases the transcription machinery requires mechanisms for correction to ensure the fidelity of the mRNA transcript. TFIIS plays a critical role by stimulating the intrinsic nuclease activity of RNA polymerase II, allowing the enzyme to cleave the recently synthesized mRNA and remove the incorrect nucleotide. After the incorrect nucleotides are removed, RNA polymerase II can resume the correct transcription of the gene.