The correct answer is letter E - Pseudomonas aeruginosa infection.

Why?

Green nails, a form of chromonychia, may be caused by bacterial infection with P. aeruginosa. This syndrome is typically seen in patients with nail disease such as onycholysis, onychotillomania, or paronychia, particularly in those whose abnormal nails have been exposed to moist environments. The green color is caused by the fluorescent siderophore pyoverdin, produced by P. aeruginosa.

Source: New England Journal of Medicine