THE OP wrote: 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.
There is no opposite of transliterate. Original substitution is what it is.
There is the original text and the transliterated text.
You would merely be substituting the original for the transliterated text. You are not recovering anything since you had to have the original to transliterate in the first place. You are replacing or substituting the original source text for the target text.
In translation, you have a source text (A) and a target text (B).
The same would be true in transliteration.
You have an original text (A) in the source language and you create a transliterated target text (B).
Back translation is completely different. Back translation seeks to compare a target language text (a translated text) with the original text. The idea is that when a not-so-good translator did the translation, she might have made errors which the back translation is supposed to reveal or catch. The method (much used in medical and technical translation, unfortunately) is very faulty as the back translator has to be very good so as not to "mis-translate" to the original and to accept that the translation being checked may have translated the actual meaning of a poorly written original. Back translation is based on the false assumption that meaning is bi-directionally equal (like two columns that can replace each other). Text A and Text B are never "equivalent" because meaning functions differently in different languages. So Text B might be a good translation of Text A, but it is never "functionally equivalent" as in a math equation.
In short, in translation and back translation, you are dealing with meaning and trying to make sure meaning is preserved.
Transliteration has nothing to do with meaning per se and everything to do with the phonetics of a language.
Going from the transliterated text to the original is simple substitution.
(People really seem to be getting their knickers in a twist about this question but as a translator, I deal with translation and back translation all the time, and transliteration has nothing to do with translation. It is most obviously: substitution or replacement.)