They can be easily heard due to the buzzing sound their wings let out. As the player gets closer and closer to one, the game screen will start to distort; then blur, and then high pitch ringing sound will start going off when they are very close.
Natalia Korda is able to see them with her special senses. She will automatically ad-lib lines telling Barry Burton when one is close. While attempting to fight one, Natalia will yell to Barry "More left!" or "Higher!" to help the player fight them. Sometimes they react to damage by dropping to the ground and flying back up.
Physical or Stealth attacks can be used on them after throwing a Smokescreen Bottle near them, which briefly give away their position. Throwing explosive bottles at their position should kill them in one hit, while Natalia can throw 2-3 bricks to take one down depending on her skill. If Claire and Moira lack any Smokescreen bottles in their Episode 4 encounter, the Glasps' tendency to knock over boxes will also give away their position.
In Raid Mode, Gabriel's Ground Pound skill is very useful to kill the Grasps in one hit without the need of detecting where they are.