I agree with Sebastian Koppehel that scrinaria in the quoted passage is a feminine singular noun derived from scrinium and the suffix -arius, -aria, -arium; this means scrinaria = scriniaria.
The omission of i after the n has no explanation in terms of the standard Latin rules of word-formation, and does not seem to be significant with respect to the meaning of the word. The spelling scrinaria might be due to accidental omission of the letter i when writing the word, or an irregular alteration in the form of the word.
-arius, -aria, -arium: a suffix that derives nouns with the form of adjectives
This suffix is a bit funny. It has the form (or morphology) of an adjective ending, but many words ending in -arius, -aria, -arium are used more frequently as substantive nouns than as attributive modifiers of other words. The masculine forms in -arius (genitive singular -arii) usually are used as the names of occupations or professions, and are highly productive in this function: thus, ferrarius = "blacksmith", gallinarius = "keeper of poultry", etc.
The gender of a form ending in -arius, -aria, -arium can sometimes be explained by interpreting it as an adjective in agreement with an "implicit" head noun: thus, aurarius used as a noun "goldsmith" could be interpreted as standing for something like "(artifex) aurarius" or "(faber) aurarius". But it isn't always clear what the implicit accompanying noun would be.
This can make the interpretation of forms a little tricky.
Scrin(i)aria probably means "Female keeper of scrinia/keeper of the scrinium"
The suggestion in Sebastian Koppehel's answer that scrinaria is feminine in agreement with gens seems plausible to me, and is in agreement with the translation "a keeper of the records" cited in Tyler Durden's answer. This is also the explanation given by Paula Fredriksen in "Anti-Judaism and Early Christianity" (Marginalia, December 9, 2013, review of David Nirenberg’s Anti-Judaism: The Western Tradition), where the word scriniaria is glossed as "[female] librarian". Fredriksen also points out there that "desks" is a mistranslation of the Latin.
It seems Fredriksen has also rendered scriniaria as "bookslave" (in Augustine and the Jews: A Christian Defense of Jews and Judaism, 2010), according to Figuring Racism in Medieval Christianity, by Lindsay Kaplan, 2019 (page 33). That translation seems to be intended to convey the overall meaning of the specific passage where the word occurs (Kaplan, page 187, provides a quote where Fredriksen (2010, page 320) argues that Augustine here is portraying the Jews as "servile book caretakers"). I don't think "bookslave" is as accurate a translation of scrin(i)aria when considered in isolation: words ending in -arius/-aria could refer to slaves, but they did not systematically denote slaves as opposed to other types of craftsmen or workers.
The meaning of scrinium "chest" (plural scrinia)
It seems a bit tricky to give a precise definition of the word scrinium. The basic literal sense seems to be chest; this can have the sense of letter-box or box of records. According to The Diplomas of King Aethlred 'the Unready' 978-1016, by Simon Keynes (1980):
The word scriniarius is ambiguous, denoting either 'archivist' or 'custodian of books' from the primary meaning of scrinium ('chest, for storage of books') or 'keeper or custodian of relics' from its secondary meaning ('reliquary' or 'shrine'). It was apparently the second meaning of scriniarius that was intended by the Abingdon glossarist, with an extension to cover the guardianship of precious things in general.
In the context of the passage quoted in your question, the "archivist" or "keeper of books/documents" sense surely fits, but perhaps it would also fit to view the word as having some connotation of "keeper of treasure/precious things".
Feminine singular nouns in -aria can sometimes have an impersonal or abstract sense; possibly it could be read as "collection/repository of scrinia"
I think an alternative possibility is that scrin(i)aria could refer to a place or location (used metaphorically in this case). Some nouns ending in -aria have that kind of meaning, such as auraria "gold-mine" or libraria "collection of books". In that case, scrin(i)aria would have a sense more like "collection/archive of scrinia". But this seems less plausible to me than the interpretation given by Paula Fredriksen and Sebastian Koppehel.
Some nouns ending in -aria have multiple possible meanings; e.g. see the Dictionary of Medieval Latin from British Sources's definition of cameraria (available via Logeion).