The form quiete is a cross reference to the following entry:
[ gdw]
The Classical Latin etymon quietus seems to have produced both quiet1 and, through a process of monophthongization, quite1. This duplication seems to have taken place before the Anglo-Norman period, with eleventh-century Latin already using quitus specifically for the sense ‘free, exempt’ alongside quietus (which has the same meaning but also retains the original sense ‘at rest, peaceful’ – derived from its origin as past participle of the verb quiescere, ‘to rest’).
The DMF treats quiet and quite as two entirely separate entries, without any overlap in sense (‘calme’ for the former, ‘Délié d'une obligation’ (etc.) for the latter), and in doing so reflects the approaches found in Gdf and TL. Modern French and English (cf. TLF and OED) confirm and validate this separation. However, as particularly the DMLBS but also the MED and the historical data of the OED show, in medieval times, the original (diphthongised) quiet form retained its wider semantic field. Whereas in AND1 the two articles were separated on the basis of sense (resulting, awkwardly, in quiet also being listed as a variant spelling of quite1), AND2 attempts to give a better indication of the medieval perception of the word(s), and returns all the diphthongised variants back under quiet1, thereby restoring the wider semantic field of this word. This same formal/etymological separation is maintained for the related entries in the dictionary.
It must be noted, however, that in Anglo-Norman this diphthongized form generally appears only in attestations from the early fourteenth-century onwards.