reasonably. Now that she is away from Ganymede’s presence, she is able to think more clearly. The archaic word quittance means a release or discharge from a debt or obligation. Just because Phoebe omitted or failed to respond to Ganymede’s hard words earlier does not mean she will forget the matter. She feels obligated to respond to those words, and she also feels (or at least hopes) that Ganymede is obligated to respond or even apologize for being so harsh.
So, Phoebe decides to write Ganymede a “taunting” or angry letter (line 135); and she asks Silvius to deliver that letter to Ganymede.