The use of inverted gi gu (i-vowel-sign) in Tibetan script can be quite baffling. There may be several explanation attempts but I would like to briefly present here Tshe-tan-zhabs-drung's explanation, which seems to be the most convincing one. For him, Tibetan inverted gi gu sign is a remnant of the short Indian (e.g. Brāhmī or Devanāgarī) i-vowel sign placed over and towards the left side of the consonant character. Compare the signs for ti and tī in the image below. The function of ’a chung (in elongating the vowel) has rendered the distinction between the gi gu sign turned to the left and the one turned to right redundant. But Tibetans continued to use inverted gi gu signs until the practice was done away in due course. See his Thon mi’i zhal lung (p. 78.11-79.16). Indeed I think we can find several other examples of such remnants to support his theory.
Some scholars have apparently tried to make a difference in the pronunciation between the inverted and non-inverted gi gus (gi gu phyir log dang phyir ma log pa) but Tshe-tan-zhabs-drung criticizes by stating that it is a futile attempt like trying to differentiate between the two eyes of a son of a barren woman (mo gsham gyi bu).
I would like to thank Arno for his very informative and illuminative comments on the inverted gi gi, which reveal that scholars have reflected for this issue for quite sometime now. Instead of trying to argue for or against one given explanation, I would like to reproduce here Arno letter which, however, did not appear in the comments section.
I presume Tshe-tan-zhabs-drung is right when tracing back the inverted gi gu to the short Indian i, but what exactly is his explanation for its use if not a difference in pronunciation long ago? Waddell had already in 1909 (“Ancient Historical Edicts at Lhasa,” JRAS, pp. 923–952) suggested “an apparent differentiation between long ī and short i, in which the short i, following its Indian Devanāgarī prototype” reversed (p. 945). This distinction between long and short vowel was entirely rejected by Laufer in 1914, see his long note on pp. 53–54 of his “Bird Divination among the Tibetans (Notes on Document Pelliot No. 3530, with a Study of Tibetan Phonology of the Ninth Century),” T’oung Pao, 15. Further on in his article Laufer has somewhat convincingly shown (p. 85) by way of Chinese transcriptions of Tibetan words that the inverted gi gu seems to have “exactly corresponded to the plain, short Chinese I,” whereas the non-inverted form was apparently pronounced differently judging by its Chinese transcription. So, after all, there does seem to be some phonetical side to the matter. I personally cannot help but feel that in many of the later texts still showing an abundance of inverted gi gus they are used on any given page in quite arbitrary a fashion, without any deeper meaning. This is obviously the weakest explanation, but who knows.
All the best,