not to give quarter

not to give quarter  {v. phr.}

1. To be utterly unwilling to show mercy; not to allow a weaker or defeated party the chance to save themselves through escape.

The occupying foreign army gave no quarter — they took no prisoners, shot everyone, and made escape impossible.

2. To argue so forcefully during a negotiation or in a court of law as to make any counter-argument or counter-proposal impossible.