In my experience (from diode laser systems I built myself and some commercial systems), if changing the piezo voltage doesn't change the wavelength, it means that your feedback into the laser is not good and probably needs to be adjusted. I'm not sure what kind of access you have to the inside of the laser (if you're not comfortable opening the system, you should call customer support if its a commercial system), but if the feedback isn't good enough, you can try to "re-flash" the laser. Again, only do this if you are comfortable opening up the system, as you can cause a lot of problems if you don't know what you're doing. Also, try to find out what your warranty is. They may not want you to open the system at all, which in that case, don't do it and call for service. If you get to a point where you need to do it though, I'll describe the procedure below. Be sure to where a wrist-strap to ground yourself to the optical table. Diode lasers will die easily from static shock, and depending on the model of laser you use, they can be either dirt cheap or really expensive.
To flash the laser, you can turn down the current of the laser to just below the lasing threshold. Using an card with a small hole in it, you should be able to put the card in front of the laser output with the beam exiting through the hole in the card. If the alignment of the grating is off, you should see that the feedback beam hits the card away from the hole. Align the grating so that the feedback beam re-enters the laser. If you align it well, the laser will then go above the lasing threshold, and you should see the output suddenly get brighter, "flashing" the laser. You can then turn down the laser current again to just below threshold and repeat this process until you flash the laser at the lowest possible current. When you turn the laser current back up to the operating current, you should have good enough feedback to tune the laser over a wide range.
For very wide tuning ranges, make sure you also temperature control the laser. It also helps to have an electronics system to change the current of the laser in tandem with the voltage to prevent mode hopping. Some commercial systems have this already on there.