You need a copper based grease to put between the pads (where the steel strips are) and the callipers - this will takeaway all noises.
Remove the brakes, give them a good clean, and reassemble but cover all contact areas with a thin layer of high temp resistant copper based grease. Our mechanics (also the authorised dealers) use ordinary grease, which melts away with high braking temperature, and this is what causes this annoying noise and this is more common with Toyota calipers due to design.
Hope this will help.