Mars-like worlds near M-dwarfs may lose air in millions of years

The criteria for finding an Earth-like planet unofficially comes down to two things: water and the habitable zone. But a phenomenon known as atmospheric escape often "escapes" the minds of many astronomy fans, and it turns out that atmospheric escape is one of the key characteristics for finding an Earth-like world. Although extensive research has been conducted on how the planet Mars might have lost its atmosphere, and potentially the ability to sustain life, how would the atmosphere enveloping a Mars-like exoplanet respond to stars different from our own?