Well, I mean did you purchase it directly from a vendor? If you were able to exchange it that might be the easiest solution. If it's preowned and you still have some contact with the previous owner you could ask them if they experienced any oddities with the touchpad.
I'm not sure there's anything you can do with software. You could download the latest driver from the ASUS page and see if it is the same, and if you can find the touchpad component manufacturer's latest driver you could try that.
If it's a physical issue you'd likely have to open the machine. You could check to see if the touchpad cable is loose or damaged. If there isn't anything obvious you might want to see if you can find a replacement on ebay.
For what it's worth I fixed the touchpad on an old G73 by applying some conductive foil tape to the back which helped with grounding but I haven't heard of anyone needing to do that on a GL55.