The Saints Know

When you gossip about a person it means you have removed the person from your heart. But be aware, when you remove a man from your heart, Jesus also goes away from your heart with that man.
 St. Padre Pio

When in doubt what to do when gossip persists against you... go to the saints, they've been there done that. 

From St. Francis de Sales (one of my absolute favorite saints):

Truth

“The first is truth to which the love of God and of ourselves in God, compels us to bear testimony. Nevertheless that testimony has to be calm, gentle, kindly, given without irritation or vehemence, and with no anxiety about consequences. Our Saviour, when He was accused of having a devil, answered quite simply, “I have not a devil” (John 8:49). If you should be blamed for any scandalous fault, of which, however, you know you are not guilty, say candidly and quietly that, by the grace of God, you are innocent of such a sin.”

Humility

“But, if you are not believed, humility now claims her right and bids you say that you have indeed many greater faults unknown to the world, that you are in every way miserable and that if God did not sustain you in your weakness, you would commit far greater crimes than you are accused of. This sort of humility is in no way prejudicial to truth, for was it not from the depths of true humility that David cried out saying, that if God had not aided him his soul would have dwelt in hell” (Ps 94:17).

Silence

“Should the tempest of evil speaking continue, silence steps to the front, and offers her calm resistance to the storm, following the teaching of the Royal Prophet, who says: And I became as a dumb man not opening his mouth [Ps 38:14]. Answering is the oil which feeds the lamp of calumny, silence is the water which extinguishes it.”

Patience

“If silence is unavailing, then patience reminds you that it is her turn to act, and, coming forward; shelters you with her impenetrable shield; patience, as Holy Scripture tells us, makes our work perfect.”

Constancy in Faith

“If we be still assailed, we must call to our aid constancy, which is a kind of double-lined buckler of patience, impervious to the most violent thrusts.”

Longanimity (long-suffering)

“But should evil tongues, growing yet sharper and keener, cut to the very quick, longanimity, which is an unfailing, undying patience, is ready to enter the lists, and eager to help us. For when persecution, instead of yielding to our patience, is only the more irritated thereby, like a fire which burns more fiercely in frosty weather, then is the time for us to practice the virtue of longanimity.”

Perseverance (if they persecuted Me, they will persecute you)

“And last of all comes perseverance, which goes with us to the very end and without which the whole network of virtues would fall to pieces; for it is the end which crowns the work, and he who perseveres to the end shall be saved.”

Charity or Love in your heart

“Indeed, who can say how many more virtues claim a place in this bright choir? Prudence, gentleness, modesty of speech, and many another, circle round their queen, holy charity, who is indeed the life and soul of them all. Charity it is which bids us bless those who curse us, and pray for those who persecute us; and this same charity not unfrequently transforms our persecutors into protectors and changes slanderous tongues into trumpets to sound our praise.”

"When we find ourselves the victim of gossip we can find great consolation in the fact that Jesus, our Savior, was himself the object of slander, calumny, gossip, and ridicule."