No quarter asked, none given - this military term came into use meaning that the victor would not be merciful. Prisoners would not be taken, the victor guaranteed death as the only option. So "no quarter" may also mean to refuse to enter into an agreement (relations) with an enemy attempting to surrender. The "quarter" seems to have originally come from the ransom of an officer, a quarter of his pay.
No mercy. This is what it means. A fight to the death. No possibility of truce. The intention being to win and to annihilate the foe. Such a contrast to a Christian walk, “Blessed are the merciful, for they will receive mercy” (Matthew 5:7).
I found this at Discover the Word that explained the difference between mercy and grace. "Grace is a loving response to people who don’t deserve it, while mercy is a loving response prompted by the misery and helplessness of the person to whom it is shown." The Bible spends a lot of time talking about God's grace towards us as in 1 Peter 4:10, "Each of you should use whatever gift you have received to serve others, as faithful stewards of God’s grace in its various forms." And how we can minister it, “Let no corrupt communication proceed out of your mouth, but that which is good to the use of edifying, that it may minister grace unto the hearers.” – Ephesians 4:29
What do you do when you are on the receiving end in a situation where you find yourself under attack by an opponent who "takes no prisoners"?