The bachelors are described as having written “from college”, suggesting that “plucked” is being used with an eye to this sense:
pluck, v. 8.a. transitive. Originally in Oxford University: to reject (a candidate) as not reaching the required standard in an examination (now historical). Later in extended use: to reject (a candidate for any examination, for office, etc.); (more generally) to call to account, to reprimand. Frequently in passive.
1837 J. R. McCulloch Statist. Acct. Brit. Empire II. v. i. 461 Those who fail in showing such an amount of proficiency as, in the opinion of the examiners, entitles them to their degree, are said, in the language of the place, to be ‘plucked’.
Oxford English Dictionary
The implication being that her correspondents showed little evidence of academic merit.
Possibly “goosequills” implies a character of fustiness or being out of date. Steel nibs, much more durable than quills, had been mass-produced since the 1820s, with sales reaching hundreds of millions annually by the 1840s.
I have a couple of thoughts about “Collegisse juvat”. First, this phrase is from the fourth line of the first Ode in the first book, and perhaps the suggestion is that this might be as far as the correspondents had got in their reading of Horace: that is, their scholarship is shallow.
Second, the choice of tag fails to be appropriate to the circumstance. For in this first ode, Horace elaborates on the commonplace idea of “to each his own taste”: that is, it pleases the politician to be elected to office, it rejoices the farmer to fill his granary, it excites the hunter when his dogs scent a deer, and first of his examples,
sunt quos curriculo pulverem Olympicum
collegisse iuvat metaque fervidis
There are those whom it delights to have gathered Olympic dust in a chariot, and the turning-post having been shaved with fiery wheels
Horace (23 BCE). Odes, book 1, ode 1, lines 3–5.
The “meta” was the pillar at each end of the “circus” or racecourse, and the charioteer who shaved it closest, without striking it and overturning, took the shortest path. In the context of Aurora Leigh, this seems quite the wrong example for the fans to have picked, for what does Aurora care about chariot-racing? A few lines later there is a much more appropriate pair of lines from which to pick a tag when writing a fan-letter to a poet:
Quod si me lyricis vatibus inseres,
sublimi feriam sidera vertice.
But if you will include me with the lyric poets, I would touch the lofty stars with my head.
Horace, lines 35–36.