What is the opposite of transliteration?

Imagine that someone takes a word in another writing system (say, the Greek word 'αγαπη') and transliterates it into the Roman alphabet (in this case, 'agapē'). Then I take that romanization and try to convert it back into its original form in the original writing system. What am I doing? I'm not transliterating 'agapē' - I'm trying to recover the original, un-transliterated version.

Example:

I'm writing a program to _ transliterated Greek words so I can easily search a Greek dictionary for them.

I am in fact writing a program that does this to transliterated Greek and am looking for some good phrasing for how to describe it. Google searches have only yielded descriptions of the difference between 'transliteration' and 'transcription', neither of which is what is happening here...

http://intranet.library.arizona.edu/users/brewerm/sil/lib/transcription.html

Definitions: Transliteration - The spelling of the words of one language with characters from the alphabet of another. Ideally, this is a character for character replacement so that reverse transliteration into the original script is possible.

You are transliterating it.

Just as with translating, if you translate something to another language, when you put it back into the first language you are also translating it - or possibly 'retranslating' or 'translating back'.

To make it more clear what you are doing I would go with 'retransliterating' or 'transliterating back'.

I'd describe it as "(trying to) recover the original Greek (from the Roman transliteration)" the first time I described it, and refer to it as "the recovered Greek" thereafter. Because, while what you are doing is an act of transliteration, the word is native to Greek, and transliteration is almost always done out of, and not into, the native alphabet. You will be continuously confusing people if you just call it transliteration.

Additionally, you may in the future decide to improve your program by looking for the closest matching Greek word from some list of valid words. It would still be accurate to describe this as "recovery", but not "transliteration".

In the generic case, it's still transliteration. It doesn't become something different just because the choice of writing systems changes (for example, it's still be transliteration to go from 東京 to طوكيو). You might, in some cases, hear 'back transliteration' (as an analogy to 'back translation', the process of translating something that was just translated back to the original language, usually to verify the quality of the translation or demonstrate issues with it) for the specific type you're doing, but that kind of implies some kind of verification of the original transliteration.

In your case, however, 'recovery of the original spelling' is what I'd go with for the description, because from what you're describing it sounds like you're dealing with words that haven't just been transliterated, but possibly been modified to allow for more 'natural' pronunciation in the target language (see for example 'waifu', which is an English transliteration of a Japanese loan of the English word 'wife', the spelling and pronunciation changed in Japanese because of the phonetic and spelling rules of the language).

How about detransliteration? It seems pretty logical.