Step 1: Think about the fate of the enamel organ after the ameloblasts finish laying down enamel. They shrink to a thin layer called the reduced enamel epithelium, which travels with the crown as it erupts.
Step 2: This reduced enamel epithelium forms the primary enamel cuticle, named Nasmyth's membrane, draped over the freshly erupted crown. It shields the enamel from resorption and secretes enzymes that clear the dental sac, allowing a bloodless eruption. Therefore Nasmyth's membrane is the covering of a newly erupted tooth.
Step 3: Rule out the distractors. Perikymata are merely the external manifestations of the incremental lines of Retzius on the enamel surface, not a membrane. Plain fibrous tissue does not specifically coat an erupted tooth. With a single correct option, 'all of the above' cannot be right.
\[\boxed{\text{Nasmyth's membrane}}\]