Normal or regular grass in the parks are not offered to Lord Ganesha.
The Durva grass is considered auspicisous and used while praying to Lord Ganehsa. It is also known as doob, the ones with 3-5 leaflets are the desirable ones. The side leaflets refer to Shiva and Shakti and the middle one is said to attract the prinicple of Ganesha. So, offering this is said to have more positive benefits. The durva grass has the ability absorb the three primal deity priniciples which the normal grass does not have.
This grass is long, has a single stem above the ground level with 3-5 nodes of spourting tender leaves. It is thin and creeps close to the ground and can grow in areas with very less water.
If you cannot buy or get Durva grass, you can offer the Arali flower (Nerium Oleander) (the reddish pink flower) or the Errukakam flower (Calotropis gigantea) or the red hibiscus flower.