The Stielhandgranate is carried by only one enemy, the Panzergrenadier. They use these stick nades to clear trenches and blow up cam nets. Damage is increased within trenches and mortar pits. Watch out for the Panzergrenadiers who use these, they will wipe out your soft defenses that are around the 200 pixel line. Stielhandgranates are very deadly against your infantry and can do minor damage to your vehicles. If you are lucky your frenchie can blow up an ammo dump and temporarily stop Panzergrenadiers's from being equipped with them.
Be wary of Panzergrenadiers in higher waves, as they can throw many grenades within a short span of time. What's even worse, since these travel in vertical lines, they can blow up anything and anyone along that line.