Grace,
xáris, is 'favor extended towards,' disposed to, inclined, leaning towards to share benefit, grace" etc.
The term 'unmerited favor' is often used of God's grace due to this verse and others like it:
"So too, at the present time there is a remnant chosen by grace. And if by grace, then it cannot be based on works; if it were, grace would no longer be grace."
Since God's favor is not based on our works, then it is 'unmerited' in that sense. However, salvific grace (as opposed to the general graces God gives to all men of Christ's death, conviction of sin, general revelation, deferring judgment, etc.) does come through faith:
"For it is by grace you have been saved, through faith--and this is not from yourselves, it is the gift of God--" Eph 2:8
What does it mean that it is by grace we have been saved, through faith, and that this is not of ourselves but is the gift of God?
"..through whom also
we have obtained our introduction by faith into this grace in which we stand; and we exult in hope of the glory of God." Rom 5:2
"For in it the righteousness of God is revealed from faith for faith, as it is written, “The righteous shall live by faith.” Rom 1:17
Etc.
Faith is not a dead work of man, rather it is trust in the person and works of Christ. It is at the point of faith which we are introduced into the grace in which we now stand (Rom 5:2) as children of God, not salvific grace that introduces us to believe. (All the general graces of God, such as Christ drawing all things to Himself at the cross or the revealed gospel, do however lead us to the point where we either believe the gospel or not.)