Moffit and Butera explain the overview of the debate:
pg. 166 "Second, in most of its occurrences, the translators of the LXX rendered [ger] with one of two words: [proselutos] or [paroikos]. Of these, they preferred [proselutos] in the vast majority of cases. While Geiger took this to imply that the Greek terms were synonymous, Allen claimed, '[T]he [LXX] version itself, when carefully examined, tells a very different tale.' As noted above, passages such as...Deut 14:21 use [paroikos] to render [ger]. According to Allen, [ger] in such passages 'cannot mean a proselyte, but must denote members of a tribe or nation sojourning in a strange land.'" (pg. 166 of "New Evidence for the Meaning and Provenance of the Word [Proselutos]" by Moffit and Butera.
pg. 174 "Allen's appeal to Exod 12:48-49 appears, therefore, to have begged the question. The claim that the translators took the [ger] to be a convert and used [proselutos] to indicate that interpretation is not proven by pointing to a passage such as Exod 12:48-49 unless one presupposes that [proselutos] means proselyte. As it stands, the Greek text, and particularly the conditional construction, effectively captures the biblical meaning of [ger]--the resident alien must be circumcised if he wants to keep Passover. Thus, these verses actually refute Allen's thesis and confirm Geiger's position--[paroikos] and [proselutos] appear to be roughly synonymous for the translators of the LXX." pg. 174 of "New Evidence for the Meaning and Provenance of the Word [Proselutos]" by Moffit and Butera.