What is the scientific name for the 'strings' between the banana peel and the fruit?

Great question! Wish I could give a "string" of citations to answer
this, but I have found only one source which gives a name to the
strings between the banana peel and the fruit. This source does not
seem very authoritative (somehow I don't like to cite someone called
"armadillogirl" as an expert on botany,) so I'm posting this as a
comment rather than an answer:

"Phloem bundles, which are the stringy things on bananas. The term is
pronounced FLOM and they carry nutrition to all parts of the banana."

http://home.att.net/~armadillogirl/ANNOYV.htm

There are many references to phloem bundles elsewhere, but I have
found no other citation that specifically relates this term to the
banana string thing.

There's a great article on Slate <http://slate.msn.com/?id=2067407> by
an economist, about from which end of a banana it makes more sense to
peel.  Unfortunately, however, it too mentions "those long stringy
things on the sides of the banana that you peel off after you remove
the skin."  Oh well.

These "strings" are composed primarily of the complex polysaccharide,
cellulose.
Probably, some starch also associated with the structures.

Your use of the term "taxonomy" is not correct.  The plant has a
taxonomic name, consisting of Genus and Species.  The sub-parts of the
plant do not. Thus, there is no  "taxonomy" of the cellulose strings.

tim, its not called taxonomy, its anatomy.  As the banana fruit is a
type of berry, am not so sure what the relevant parts are called,
maybe you could check out some sites that contain fruit--anatomy
information?