The key to reducing damage from the explosion is moving away from it or moving behind cover, and how doable that is will depend on the interaction of movement rules with the time and position of the explosion.
Eclipse Phase's native system (unless I'm missing a rule outside the core combat ruleset) doesn't have a rule that allows reflexively taking a movement quick action on an enemy's turn as you dodge. (This contrasts with systems such as GURPS, where a character may usually move one yard when dodging an enemy attack.)
As a result, there's very little that can be done if a grenade or seeker is instant-detonation (airburst, impact, or even signal triggered mid-flight). This is actually quite plausible: even thrown grenades tend to move rather fast, and the time between it passing a (missed) direct hit point and reaching the detonation distance, getting a detonation signal, or impacting the nearby surface, is likely to be in the hundredths or at most a couple tenths of a second; meanwhile, a even a transhuman morph just can't even accelerate to a necessary speed to move an appreciable distance away in that time frame.
So be glad if you at least managed to avoid a direct impact, and make sure you're not late on your morph insurance payments.
Things get drastically better for the defender in this scenario.
Eclipse Phase corebook, page 200
The minimum detonation
period—1 second—means that the munition will
detonate on the user’s (current) Initiative Score in the
next Action Phase.
In this case, the ability or inability to reduce or avoid an explosion emerges naturally out of the movement, speed and initiative rules.
If, after the grenade was thrown, the defender is eligible to perform more actions, it can use the next such opportunity to make a run for it.
- If the defender has a lower initiative than the attacker, then it can move out of the way during the same Action Phase.
- If the defender's initiative is better than the attacker's, but the defender has enough Speed to act the next Action Phase of the same Action Turn, then it can get out of the way during the aforementioned next Action Phase in this Action Turn.
- If the grenade was thrown in the last Action Phase of the Action Turn, then the next Action Phase occurs in the next Action Turn, and the ability to take a defensive action before the grenade explodes will depend on the initiative roll in the next Action Turn.
- If the defender lacks the Speed to act in the next Action Phase of the Action Turn, then the grenade falls to the ground (wherever the scatter indicates), and explodes too soon for the defender to get out of the way.
Just how far the defender moves out of the way will of course depend on the movement method chosen (walk, run, jump), obstacles in the way etc.