Logo Vectorization and Cleanup

I need assistance with separating two logos from one file into two distinct vector files. Additionally, both logos require cleaning up.

Key Requirements:
- Separate the two logos into individual vector files.
- Clean up the logos by removing the background and refining the edges.
- Deliver the final vector files in EPS format.
- Maintain the current size and dimensions of the logos.

Ideal Skills and Experience:
- Proficiency in vector graphic software, particularly Adobe Illustrator.
- Experience in logo design and cleanup.
- Attention to detail in refining and enhancing logo quality.