Construct 2's image editor does not add a 1px space to tiled background images.
This is an issue with how GPUs draw tiled textures, and is not specific to Construct 2, you'll have this problem regardless of what tool you use. Usually it's caused by sub-pixel positioning or non-power-of-two textures. At the moment only power-of-two size textures can be tiled perfectly and seamlessly (the image editor should warn you if using a non-power-of-two size). Also, enabling 'pixel rounding' in project properties will prevent sub-pixel positioning so seams never appear, but it could make scrolling a little less smooth.
Pixel Rounding and power of 2 doesn't make any difference for me, unfortunately :/
Same problem. But It doesn't show on my AMD gfx machine and my Nvidia machine with older drivers.
So it could be a driver problem with Nvidias latest drivers.