You have misunderstood the scripture you recite.
Faith is not the gift here, salvation is. You could read the sentence this way, "Through YOUR FAITH you have been saved by grace, and this is not your own doing, or WORKS. Salvation is the gift of God so that no one may boast."
You have also misunderstood the definition of work. Mowing the lawn, shoveling snow, "or in this context" following the mosaic "laws of sacrifice" are examples of work. Work is labor.
Faith, on the other hand, is our response to Gods invitation to come nearer to Him.
We must have faith, for through faith comes grace and salvation.
"Therefore produce fruit that proves your repentance," says John the baptist. Is "producing fruit" works?
The Greek word there is
ergon, which refers to work, act, effort. Anything that we do is work. If the faith is something we do, then that is of ourselves and we would have occasion to boast. Faith is a gift, the Apostle says, "Faith comes by hearing, and hearing by the word of Christ", faith is not something we offer, or contribute, or do; faith is not something we have already in us by which we can turn to God in our own strength to please Him; faith is what God gives us, it is God's work, God's gift.
If faith is "my part" then I have something to boast in don't I? After all I helped, I contributed, I met God halfway and we did this me getting saved thing together, so I should get at least some credit for it.
But that's not what the Apostle says. The Apostle says we have nothing to boast about, because this isn't of ourselves, it is the gift of God--the whole thing, all of it, every last bit of it is God's gift, God's work, and thus we can; as he says elsewhere, boast in nothing save for the cross of Jesus Christ.
Christ has done everything.
I've done nothing.
Glory to Him alone.
Solus Christus, Soli Deo Gloria.
-CryptoLutheran